In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers.

Informally speaking, the prime number theorem states that if a random integer is selected near to some large integer ''N'', the probability that the selected integer is prime is about 1 / ln(''N''), where ln(''N'') denotes the natural logarithm of ''N''. For example, near ''N'' = 1,000, about one in seven numbers is prime, whereas near ''N'' = 10,000,000,000, about one in 23 numbers is prime. In other words, the average gap between consecutive prime numbers near ''N'' is roughly ln(''N'').

Statement of the theorem

Let π(''x'') be the prime-counting function that gives the number of primes less than or equal to ''x'', for any real number ''x''. For example, π(10) = 4 because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10. The prime number theorem then states that the limit of the ''quotient'' of the two functions π(''x'') and ''x'' / ln(''x'') as ''x'' approaches infinity is 1, which is expressed by the formula

: $\backslash lim\_\{x\backslash to\backslash infty\}\backslash frac\{\backslash pi(x)\}\{x/\backslash ln(x)\}=1,$

known as the asymptotic law of distribution of prime numbers. Using asymptotic notation this result can be restated as

:$\backslash pi(x)\backslash sim\backslash frac\{x\}\{\backslash ln\; x\}.\backslash !$

This notation (and the theorem) does ''not'' say anything about the limit of the ''difference'' of the two functions as ''x'' approaches infinity. (Indeed, the behavior of this difference is very complicated and related to the Riemann hypothesis.) Instead, the theorem states that ''x''/ln(''x'') approximates π(''x'') in the sense that the relative error of this approximation approaches 0 as ''x'' approaches infinity.

The prime number theorem is equivalent to the statement that the ''n''th prime number ''p''_''n'' is approximately equal to ''n'' ln(''n''), again with the relative error of this approximation approaching 0 as ''n'' approaches infinity.

History of the asymptotic law of distribution of prime numbers and its proof

Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 (year VI of the french republican calendar) that π(''a'') is approximated by the function ''a''/(A ln(''a'')+''B''), where ''A'' and B are unspecified constants. In the second edition of his book on number theory (1808) he then made a more precise conjecture, with ''A''=1 and ''B''= -1.08366. Carl Friedrich Gauss considered the same question: "Ins Jahr 1792 oder 1793", according to his own recollection nearly sixty years later in a letter to Encke (1849), he wrote in his logarithm table (he was then 15 or 16) the short note "Primzahlen unter $a(=\backslash infty)\; \backslash frac\; a\{\backslash ln\; a\}$". But Gauss never published this conjecture. In 1838 Johann Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(''x'') (under the slightly different form of a series, which he communicated to Gauss). Both Legendre's and Dirichlet's's formulas imply the same conjectured asymptotic equivalence of π(''x'') and ''x'' / ln(''x'') stated above, although it turned out that Dirichlet's approximation is considerably better if one considers the differences instead of quotients.

In two papers from 1848 and 1850, the Russian mathematician Pafnuty L'vovich Chebyshev attempted to prove the asymptotic law of distribution of prime numbers. His work is notable for the use of the zeta function ζ(''s'') (for real values of the argument "s", as are works of Leonhard Euler, as early as 1737) predating Riemann's celebrated memoir of 1859, and he succeeded in proving a slightly weaker form of the asymptotic law, namely, that if the limit of π(''x'')/(''x''/ln(''x'')) as ''x'' goes to infinity exists at all, then it is necessarily equal to one. He was able to prove unconditionally that this ratio is bounded above and below by two explicitly given constants near to 1 for all ''x''. Although Chebyshev's paper did not prove the Prime Number Theorem, his estimates for π(''x'') were strong enough for him to prove Bertrand's postulate that there exists a prime number between ''n'' and ''2n'' for any integer ''n'' ≥ 2.

Without doubt, the single most significant paper concerning the distribution of prime numbers was Riemann's 1859 memoir ''On the Number of Primes Less Than a Given Magnitude'', the only paper he ever wrote on the subject. Riemann introduced revolutionary ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the analytically extended Riemann zeta function of a complex variable. In particular, it is in this paper of Riemann that the idea to apply methods of complex analysis to the study of the real function π(''x'') originates. Extending these deep ideas of Riemann, two proofs of the asymptotic law of the distribution of prime numbers were obtained independently by Hadamard and de la Vallée Poussin and appeared in the same year (1896). Both proofs used methods from complex analysis, establishing as a main step of the proof that the Riemann zeta function ζ(''s'') is non-zero for all complex values of the variable ''s'' that have the form ''s'' = 1 + ''it'' with ''t'' > 0.

During the 20th century, the theorem of Hadamard and de la Vallée-Poussin also became known as the Prime Number Theorem. Several different proofs of it were found, including the "elementary" proofs of Atle Selberg and Paul Erdős (1949). While the original proofs of Hadamard and de la Vallée-Poussin are long and elaborate, and later proofs have introduced various simplifications through the use of Tauberian theorems but remained difficult to digest, a surprisingly short proof was discovered in 1980 by American mathematician Donald J. Newman. Newman's proof is arguably the simplest known proof of the theorem, although it is non-elementary in the sense that it uses Cauchy's integral theorem from complex analysis.

Proof methodology

In a lecture on prime numbers for a general audience, Fields medalist Terence Tao described one approach to proving the prime number theorem in poetic terms: listening to the "music" of the primes. We start with a "sound wave" that is "noisy" at the prime numbers and silent at other numbers; this is the von Mangoldt function. Then we analyze its notes or frequencies by subjecting it to a process akin to Fourier transform; this is the Mellin transform. Then we prove, and this is the hard part, that certain "notes" cannot occur in this music. This exclusion of certain notes leads to the statement of the prime number theorem. According to Tao, this proof yields much deeper insights into the distribution of the primes than the "elementary" proofs discussed below.

Proof sketch

Here is a sketch of the proof referred to in Tao's lecture mentioned above. Like most proofs of the PNT, it starts out by reformulating the problem in terms of a less intuitive, but better-behaved, prime-counting function. The idea is to count the primes (or a related set such as the set of prime powers) with ''weights'' to arrive at a function with smoother asymptotic behavior. The most common such generalized counting function is the Chebyshev function $\backslash psi(x)$, defined by

:$\backslash psi(x)\; =\; \backslash sum\_\{p^k\; \backslash le\; x\}\; \backslash log\; p.$ Here the summation is over all prime powers up to ''x''. This is sometimes written as $\backslash psi(x)=\backslash sum\_\{n\backslash le\; x\}\; \backslash Lambda(n)$, where $\backslash Lambda(n)$ is the von Mangoldt function, namely

:

It is now relatively easy to check that the PNT is equivalent to the claim that $\backslash lim\_\{x\backslash to\backslash infty\}\; \backslash psi(x)/x=1$. Indeed, this follows from the easy estimates :$\backslash psi(x)\; =\; \backslash sum\_\{p\backslash le\; x\}\; \backslash log\; p\; \backslash left\backslash lfloor\; \backslash frac\{\backslash log\; x\}\{\backslash log\; p\}\; \backslash right\backslash rfloor\; \backslash le\; \backslash sum\_\{p\backslash le\; x\}\; \backslash log\; x\; =\; \backslash pi(x)\backslash log\; x$ and (using big O notation) for any ε > 0, :$\backslash psi(x)\; \backslash ge\; \backslash sum\_\{x^\{1-\backslash epsilon\}\backslash le\; p\backslash le\; x\}\; \backslash log\; p\backslash ge\backslash sum\_\{x^\{1-\backslash epsilon\}\backslash le\; p\backslash le\; x\}(1-\backslash epsilon)\backslash log\; x=(1-\backslash epsilon)(\backslash pi(x)+O(x^\{1-\backslash epsilon\}))\backslash log\; x.$

The next step is to find a useful representation for $\backslash psi(x)$. Let $\backslash zeta(s)$ be the Riemann zeta function. It can be shown that $\backslash zeta(s)$ is related to the von Mangoldt function $\backslash Lambda(n)$, and hence to $\backslash psi(x)$, via the relation

:$-\backslash frac\{\backslash zeta\text{'}(s)\}\{\backslash zeta(s)\}\; =\; \backslash sum\_\{n\; =\; 1\}^\backslash infty\; \backslash Lambda(n)\; n^\{-s\}.$

A delicate analysis of this equation and related properties of the zeta function, using the Mellin transform and Perron's formula, shows that for non-integer ''x'' the equation

:$\backslash psi(x)\; =\; x\; -\; \backslash sum\_\{\backslash rho\}\; \backslash frac\{x^\backslash rho\}\{\backslash rho\}\; -\; \backslash log(2\backslash pi)$

holds, where the sum is over all zeros (trivial and non-trivial) of the zeta function. This striking formula is one of the so-called explicit formulas of number theory, and is already suggestive of the result we wish to prove, since the term ''x'' (claimed to be the correct asymptotic order of $\backslash psi(x)$) appears on the right-hand side, followed by (presumably) lower-order asymptotic terms.

The next step in the proof involves a study of the zeros of the zeta function. The trivial zeros −2, −4, −6, −8, ... can be handled separately: :$\backslash sum\_\{n=1\}^\backslash infty\; \backslash frac\{1\}\{2n\backslash ,x^\{2n\}\}\; =\; -\backslash frac\{1\}\{2\}\backslash ln\backslash left(1-\backslash frac\{1\}\{x^2\}\backslash right),$ which vanishes for a large ''x''. The nontrivial zeros, namely those on the critical strip $0\backslash le\; \backslash Re(s)\backslash le\; 1$, can potentially be of an asymptotic order comparable to the main term ''x'' if $\backslash Re(\backslash rho)=1$, so we need to show that all zeros have real part strictly less than 1.

To do this, we take for granted that $\backslash zeta(s)$ is meromorphic in the half-plane $\backslash Re(s)>0$, and is analytic there except for a simple pole at $s=1$, and that there is a product formula $\backslash zeta(s)=\backslash prod\_p(1-p^\{-s\})^\{-1\}$ for $\backslash Re(s)>1.$ This product formula follows from the existence of unique prime factorization of integers, and shows that $\backslash zeta(s)$ is never zero in this region, so that its logarithm is defined there and $\backslash log\backslash zeta(s)=-\backslash sum\_p\backslash log\; (1-p^\{-s\}\; )=\backslash sum\_\{p,n\}p^\{-ns\}/n.$ Write $s=x+iy$; then

$|\backslash zeta(x+iy)|=\backslash exp(\backslash sum\_\{n,p\}\backslash frac\{\backslash cos\; ny\backslash log\; p\}\{np^\{nx\}\}).$

Now observe the identity $3+4\backslash cos\backslash phi+\backslash cos2\backslash phi=2(1+\backslash cos\backslash phi)^2\backslash ge\; 0,$ so that

$|\backslash zeta(x)^3\backslash zeta(x+iy)^4\backslash zeta(x+2iy)|=\backslash exp\backslash sum\_\{n,p\}\backslash frac\{3+4\backslash cos(ny\backslash log\; p)\; +\backslash cos\; (2ny\backslash log\; p)\}\{np^\{nx\}\}\backslash ge\; 1$

for all $x>\; 1$. Suppose now that $\backslash zeta(1+iy)=0$. Certainly $y$ is not zero, since $\backslash zeta(s)$ has a simple pole at $s=1$. Suppose that $x>1$ and let $x$ tend to $1$ from above. Since $\backslash zeta(s)$ has a simple pole at $s=1$ and $\backslash zeta(x+2iy)$ stays analytic, the left hand side in the previous inequality tends to $0$, a contradiction.

Finally, we can conclude that the PNT is "morally" true. To rigorously complete the proof there are still serious technicalities to overcome, due to the fact that the summation over zeta zeros in the explicit formula for $\backslash psi(x)$ does not converge absolutely but only conditionally and in a "principal value" sense. There are several ways around this problem but all of them require rather delicate complex-analytic estimates that are beyond the scope of this article. Edwards's book provides the details.

The prime-counting function in terms of the logarithmic integral

In a handwritten note on a reprint of his 1838 paper "Sur l'usage des séries infinies dans la théorie des nombres", which he mailed to Carl Friedrich Gauss, Johann Peter Gustav Lejeune Dirichlet conjectured (under a slightly different form appealing to a series rather than an integral) that an even better approximation to π(''x'') is given by the offset logarithmic integral function Li(''x''), defined by

:$\backslash mathrm\{Li\}(x)\; =\; \backslash int\_2^x\; \backslash frac1\{\backslash ln\; t\}\; \backslash ,\backslash mathrm\{d\}t\; =\; \backslash mathrm\{li\}(x)\; -\; \backslash mathrm\{li\}(2).$

Indeed, this integral is strongly suggestive of the notion that the 'density' of primes around ''t'' should be 1/ln''t''. This function is related to the logarithm by the asymptotic expansion

:$\backslash mathrm\{Li\}(x)\; \backslash sim\; \backslash frac\{x\}\{\backslash ln\; x\}\; \backslash sum\_\{k=0\}^\backslash infty\; \backslash frac\{k!\}\{(\backslash ln\; x)^k\}\; =\; \backslash frac\{x\}\{\backslash ln\; x\}\; +\; \backslash frac\{x\}\{(\backslash ln\; x)^2\}\; +\; \backslash frac\{2x\}\{(\backslash ln\; x)^3\}\; +\; \backslash cdots.$

So, the prime number theorem can also be written as π(''x'') ~ Li(''x''). In fact, it follows from the proof of Hadamard and de la Vallée Poussin that

:$\backslash pi(x)=\{\backslash rm\; Li\}\; (x)\; +\; O\; \backslash left(x\; \backslash mathrm\{e\}^\{-a\backslash sqrt\{\backslash ln\; x\}\}\backslash right)\; \backslash quad\backslash text\{as\; \}\; x\; \backslash to\; \backslash infty$

for some positive constant ''a'', where ''O''(…) is the big O notation. This has been improved to

:$\backslash pi(x)=\{\backslash rm\; Li\}\; (x)\; +\; O\; \backslash left(x\; \backslash ,\; \backslash exp\; \backslash left(\; -\backslash frac\{A(\backslash ln\; x)^\{3/5\}\}\{(\backslash ln\; \backslash ln\; x)^\{1/5\}\}\; \backslash right)\; \backslash right).$

Because of the connection between the Riemann zeta function and π(''x''), the Riemann hypothesis has considerable importance in number theory: if established, it would yield a far better estimate of the error involved in the prime number theorem than is available today. More specifically, Helge von Koch showed in 1901 that, if and only if the Riemann hypothesis is true, the error term in the above relation can be improved to

:$\backslash pi(x)\; =\; \{\backslash rm\; Li\}\; (x)\; +\; O\backslash left(\backslash sqrt\; x\; \backslash ln\; x\backslash right).$

The constant involved in the big O notation was estimated in 1976 by Lowell Schoenfeld: assuming the Riemann hypothesis,

:

for all ''x'' ≥ 2657. He also derived a similar bound for the Chebyshev prime-counting function ψ:

:

for all ''x'' ≥ 73.2.

The logarithmic integral Li(''x'') is larger than π(''x'') for "small" values of ''x''. This is because it is (in some sense) counting not primes, but prime powers, where a power ''p''^''n'' of a prime ''p'' is counted as 1/''n'' of a prime. This suggests that Li(''x'') should usually be larger than π(''x'') by roughly Li(''x''^1/2)/2, and in particular should usually be larger than π(''x''). However, in 1914, J. E. Littlewood proved that this is not always the case. The first value of ''x'' where π(''x'') exceeds Li(''x'') is probably around ''x'' = 10³¹⁶; see the article on Skewes' number for more details.

Elementary proofs

In the first half of the twentieth century, some mathematicians (notably G. H. Hardy) believed that there exists a hierarchy of proof methods in mathematics depending on what sorts of numbers (integers, reals, complex) a proof requires, and that the prime number theorem (PNT) is a "deep" theorem by virtue of requiring complex analysis. This belief was somewhat shaken by a proof of the PNT based on Wiener's tauberian theorem, though this could be set aside if Wiener's theorem were deemed to have a "depth" equivalent to that of complex variable methods. There is no rigorous and widely accepted definition of the notion of elementary proof in number theory. One definition is "a proof that can be carried out in first order Peano arithmetic." There are theorems of Peano arithmetic (for example, the Paris-Harrington theorem) provable using second order but not first order methods, but such theorems are rare to date.

In March 1948, Atle Selberg established, by elementary means, the asymptotic formula :$\backslash vartheta\; \backslash left(\; x\; \backslash right)\backslash log\; \backslash left(\; x\; \backslash right)\; +\; \backslash sum\backslash limits\_\{p\; \backslash le\; x\}\; \{\backslash log\; \backslash left(\; p\; \backslash right)\}\; \backslash vartheta\; \backslash left(\; \{\backslash frac\{x\}\{p\}\}\; \backslash right)\; =\; 2x\backslash log\; \backslash left(\; x\; \backslash right)\; +\; O\backslash left(\; x\; \backslash right)$

where :$\backslash vartheta\; \backslash left(\; x\; \backslash right)\; =\; \backslash sum\backslash limits\_\{p\; \backslash le\; x\}\; \{\backslash log\; \backslash left(\; p\; \backslash right)\}$

for primes $p$. By July of that year, Selberg and Paul Erdős had each obtained elementary proofs of the PNT, both using Selberg's asymptotic formula as a starting point. These proofs effectively laid to rest the notion that the PNT was "deep," and showed that technically "elementary" methods (in other words Peano arithmetic) were more powerful than had been believed to be the case. In 1994, Charalambos Cornaros and Costas Dimitracopoulos proved the PNT using only $I\backslash Delta\_0+\backslash exp$, a formal system far weaker than Peano arithmetic. On the history of the elementary proofs of the PNT, including the Erdős–Selberg priority dispute, see Dorian Goldfeld.

Computer proofs

In 2005, Avigad ''et al.'' employed the Isabelle theorem prover to devise a computer-verified variant of the Erdős–Selberg proof of the PNT. This was the first machine-verified proof of the PNT. Avigad chose to formalize the Erdős-Selberg proof rather than an analytic one because while Isabelle's library at the time could implement the notions of limit, derivative, and transcendental function, it had almost no theory of integration to speak of (Avigad et al. p. 19).

In 2009, John Harrison employed HOL Light to formalize a proof employing complex analysis. By developing the necessary analytic machinery, including the Cauchy integral formula, Harrison was able to formalize “a direct, modern and elegant proof instead of the more involved ‘elementary’ Erdös-Selberg argument.”

The prime number theorem for arithmetic progressions

Let $\backslash pi\_\{n,a\}(x)$ denote the number of primes in the arithmetic progression ''a'', ''a'' + ''n'', ''a'' + 2''n'', ''a'' + 3''n'', … less than ''x''. Dirichlet and Legendre conjectured, and Vallée-Poussin proved, that, if ''a'' and ''n'' are coprime, then :$\backslash pi\_\{n,a\}(x)\; \backslash sim\; \backslash frac\{1\}\{\backslash phi(n)\}\backslash mathrm\{Li\}(x),$ where φ(·) is the Euler's totient function. In other words, the primes are distributed evenly among the residue classes [''a''] modulo ''n'' with gcd(''a'', ''n'') = 1. This can be proved using similar methods used by Newman for his proof of the prime number theorem.

Although we have in particular :$\backslash pi\_\{4,1\}(x)\; \backslash sim\; \backslash pi\_\{4,3\}(x),\; \backslash ,$ empirically the primes congruent to 3 are more numerous and are nearly always ahead in this "prime number race"; the first reversal occurs at ''x'' = 26,861. However Littlewood showed in 1914 that there are infinitely many sign changes for the function :$\backslash pi\_\{4,1\}(x)\; -\; \backslash pi\_\{4,3\}(x),\; \backslash ,$ so the lead in the race switches back and forth infinitely many times. The phenomenon that π_4,3(''x'') is ahead most of the time is called Chebyshev's bias. The prime number race generalizes to other moduli and is the subject of much research; Granville and Martin give a thorough exposition and survey.

Bounds on the prime-counting function

The prime number theorem is an ''asymptotic'' result. Hence, it cannot be used to ''bound'' π(''x'').

However, some bounds on π(''x'') are known, for instance Pierre Dusart's : The first inequality holds for all ''x'' ≥ 599 and the second one for ''x'' ≥ 355991.

A weaker but sometimes useful bound is : for ''x'' ≥ 55. In Dusart's thesis there are stronger versions of this type of inequality that are valid for larger ''x''.

The proof by de la Vallée-Poussin implies the following. For every ε > 0, there is an ''S'' such that for all ''x'' > ''S'', :

Approximations for the ''n''th prime number

As a consequence of the prime number theorem, one gets an asymptotic expression for the ''n''th prime number, denoted by ''p''_''n'': :$p\_n\; \backslash sim\; n\; \backslash ln\; n.$ A better approximation is :$\{\; p\_n\; =\; n\; \backslash ln\; n\; +\; n\; \backslash ln\; \backslash ln\; n\; -\; n\; +\; \backslash frac\{n\}\{\backslash ln\; n\}\; \backslash left(\backslash ln\; \backslash ln\; n\; -\; 2\; \backslash right)\; -\; \backslash frac\{n\backslash ln\backslash ln\; n\}\{2(\backslash ln\; n)^2\}\backslash left(\backslash ln\backslash ln\; n-6\backslash right)\; +\; O\backslash left(\; \backslash frac\; \{n\}\; \{(\backslash ln\; n)^2\}\backslash right).\}$

Rosser's theorem states that ''p''_''n'' is larger than ''n'' ln ''n''. This can be improved by the following pair of bounds: :

Table of π(''x''), ''x'' / ln ''x'', and li(''x'')

The table compares exact values of π(''x'') to the two approximations ''x'' / ln ''x'' and li(''x''). The last column, ''x'' / π(''x''), is the average prime gap below ''x''. :{| class="wikitable" style="text-align: right" ! ''x'' ! π(''x'') ! π(''x'') − ''x'' / ln ''x'' ! π(''x'') / (''x'' / ln ''x'') ! li(''x'') − π(''x'') ! ''x'' / π(''x'') |- | 10 | 4 | −0.3 | 0.921 | 2.2 | 2.500 |- | 10² | 25 | 3.3 | 1.151 | 5.1 | 4.000 |- | 10³ | 168 | 23 | 1.161 | 10 | 5.952 |- | 10⁴ | 1,229 | 143 | 1.132 | 17 | 8.137 |- | 10⁵ | 9,592 | 906 | 1.104 | 38 | 10.425 |- | 10⁶ | 78,498 | 6,116 | 1.084 | 130 | 12.740 |- | 10⁷ | 664,579 | 44,158 | 1.071 | 339 | 15.047 |- | 10⁸ | 5,761,455 | 332,774 | 1.061 | 754 | 17.357 |- | 10⁹ | 50,847,534 | 2,592,592 | 1.054 | 1,701 | 19.667 |- | 10¹⁰ | 455,052,511 | 20,758,029 | 1.048 | 3,104 | 21.975 |- | 10¹¹ | 4,118,054,813 | 169,923,159 | 1.043 | 11,588 | 24.283 |- | 10¹² | 37,607,912,018 | 1,416,705,193 | 1.039 | 38,263 | 26.590 |- | 10¹³ | 346,065,536,839 | 11,992,858,452 | 1.034 | 108,971 | 28.896 |- | 10¹⁴ | 3,204,941,750,802 | 102,838,308,636 | 1.033 | 314,890 | 31.202 |- | 10¹⁵ | 29,844,570,422,669 | 891,604,962,452 | 1.031 | 1,052,619 | 33.507 |- | 10¹⁶ | 279,238,341,033,925 | 7,804,289,844,393 | 1.029 | 3,214,632 | 35.812 |- | 10¹⁷ | 2,623,557,157,654,233 | 68,883,734,693,281 | 1.027 | 7,956,589 | 38.116 |- | 10¹⁸ | 24,739,954,287,740,860 | 612,483,070,893,536 | 1.025 | 21,949,555 | 40.420 |- | 10¹⁹ | 234,057,667,276,344,607 | 5,481,624,169,369,960 | 1.024 | 99,877,775 | 42.725 |- | 10²⁰ | 2,220,819,602,560,918,840 | 49,347,193,044,659,701 | 1.023 | 222,744,644 | 45.028 |- | 10²¹ | 21,127,269,486,018,731,928 | 446,579,871,578,168,707 | 1.022 | 597,394,254 | 47.332 |- | 10²² | 201,467,286,689,315,906,290 | 4,060,704,006,019,620,994 | 1.021 | 1,932,355,208 | 49.636 |- | 10²³ | 1,925,320,391,606,803,968,923 | 37,083,513,766,578,631,309 | 1.020 | 7,250,186,216 | 51.939 |}

Analogue for irreducible polynomials over a finite field

There is an analogue of the prime number theorem that describes the "distribution" of irreducible polynomials over a finite field; the form it takes is strikingly similar to the case of the classical prime number theorem.

To state it precisely, let ''F'' = GF(''q'') be the finite field with ''q'' elements, for some fixed ''q'', and let ''N''_''n'' be the number of monic ''irreducible'' polynomials over ''F'' whose degree is equal to ''n''. That is, we are looking at polynomials with coefficients chosen from ''F'', which cannot be written as products of polynomials of smaller degree. In this setting, these polynomials play the role of the prime numbers, since all other monic polynomials are built up of products of them. One can then prove that :$N\_n\; \backslash sim\; \backslash frac\{q^n\}\{n\}.$ If we make the substitution ''x'' = ''q''^''n'', then the right hand side is just :$\backslash frac\{x\}\{\backslash log\_q\; x\},$ which makes the analogy clearer. Since there are precisely ''q''^''n'' monic polynomials of degree ''n'' (including the reducible ones), this can be rephrased as follows: if a monic polynomial of degree ''n'' is selected randomly, then the probability of it being irreducible is about 1/''n''.

One can even prove an analogue of the Riemann hypothesis, namely that :$N\_n\; =\; \backslash frac\{q^n\}n\; +\; O\backslash left(\backslash frac\{q^\{n/2\}\}\{n\}\backslash right).$

The proofs of these statements are far simpler than in the classical case. It involves a short combinatorial argument, summarised as follows. Every element of the degree ''n'' extension of ''F'' is a root of some irreducible polynomial whose degree ''d'' divides ''n''; by counting these roots in two different ways one establishes that :$q^n\; =\; \backslash sum\_\{d\backslash mid\; n\}\; d\; N\_d,$ where the sum is over all divisors ''d'' of ''n''. Möbius inversion then yields :$N\_n\; =\; \backslash frac1n\; \backslash sum\_\{d\backslash mid\; n\}\; \backslash mu(n/d)\; q^d,$ where μ(''k'') is the Möbius function. (This formula was known to Gauss.) The main term occurs for ''d'' = ''n'', and it is not difficult to bound the remaining terms. The "Riemann hypothesis" statement depends on the fact that the largest proper divisor of ''n'' can be no larger than ''n''/2.

See also

Abstract analytic number theory for information about generalizations of the theorem.

Landau prime ideal theorem for a generalization to prime ideals in algebraic number fields.

Notes

References

External links

Table of Primes by Anton Felkel.

Prime formulas and Prime number theorem at MathWorld.

How Many Primes Are There? and The Gaps between Primes by Chris Caldwell, University of Tennessee at Martin.

Tables of prime-counting functions by Tomás Oliveira e Silva

Category:Analytic number theory Category:Mathematical theorems Category:Prime numbers

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Debutyear	2000
Debutteam	New England Patriots
Highlights	Rated #21 NFL Player of all-time by NFL.com as of 2009 season 6× Pro Bowl selection (2001, 2004, 2005, 2007, 2009, 2010) 2× First-team All-Pro selection (2007, 2010) 1× Second-team All-Pro selection (2005) 3× Super Bowl champion (XXXVI, XXXVIII, XXXIX) 2× Super Bowl MVP (XXXVI, XXXVIII) Sportsman of the Year (2005) SI NFL POY (x1) Sporting News Sportsman of the Year (2004, 2007) AP Male Athlete of the Year (2007) 2× AP NFL MVP (2007, 2010) 2× AP NFL Offensive Player of the Year (2007, 2010) AFC Offensive Player of the Year (2007) NFL Comeback Player of the Year (2009) New England Patriots All-time leader (Passing touchdowns) NFL 2000s All-Decade Team List of his accomplishments
College	Michigan
Draftyear	2000
Draftround	6
Draftpick	199
Pastteams	New England Patriots (–present)
Status	Active
Statseason	2010
Statlabel1	Pass attempts
Statvalue1	4,710
Statlabel2	Pass completions
Statvalue2	2,996
Statlabel3	Percentage
Statvalue3	63.6
Statlabel4	TD–INT
Statvalue4	261–103
Statlabel5	Passing yards
Statvalue5	34,744
Statlabel6	QB Rating
Statvalue6	95.2
Nfl	BRA371156 }}

Thomas Edward Patrick "Tom" Brady, Jr. (born August 3, 1977) is an American football quarterback for the New England Patriots of the National Football League (NFL). After playing college football at Michigan, Brady was drafted by the Patriots in the sixth round of the 2000 NFL Draft.

He has played in four Super Bowls, winning three of them (XXXVI, XXXVIII, XXXIX). He has also won two Super Bowl MVP awards (XXXVI and XXXVIII), has been selected to six Pro Bowls (and invited to seven, although he declined the 2006 invitation), and holds the NFL record for most touchdown passes in a single regular season. His career postseason record is 14–5. He also helped set the record for the longest consecutive win streak in NFL history with 21 straight wins over two seasons (2003–04), and in 2007 he led the Patriots to the first undefeated regular season since the institution of the 16-game schedule. Brady has the fifth-highest career passer rating of all time (95.2) among quarterbacks with at least 1,500 career passing attempts. He, along with Joe Montana, are the only two players in NFL history to have won multiple NFL MVP and Super Bowl MVP awards (2 NFL MVPs, 2 Super Bowl MVPs).

He was named ''Sports Illustrated's'' Sportsman of the Year in 2005, and was named "Sportsman of the Year" by ''The Sporting News'' in 2004 and 2007. He was also named the 2007 and 2010 NFL MVP (becoming in the 2010 season the first player to be unanimously chosen as MVP) as well as 2007 Male Athlete of the Year by the Associated Press, the first time an NFL player has been honored since Joe Montana won in 1990.

Brady holds numerous regular season and postseason records, including: most touchdown passes in a regular season (50); highest touchdown-to-interception ratio in a single season (9:1); highest single-game completion percentage, regular season or postseason (26/28, 92.9%); most consecutive pass attempts without an interception (339, still active); most consecutive regular-season home wins (28, still active); highest winning percentage of any quarterback ever during his first 100 starts (76 wins); most completions in one Super Bowl (32); and the longest streak of games with 3 or more touchdown passes (10 games). most career completions in Super Bowl history (100); Brady is the fourth-fastest player to reach 200 career passing touchdowns (116 games). He is the first quarterback in NFL history to have reached said mark with under 100 career interceptions (he had 88 interceptions). Considering his many numerous achievements, and his late draft selection (6th round, 199th selection), many analysts, including those at the NFL Network, have called Brady the best NFL draft pick (or draft steal) of all time, as well as one of the greatest quarterbacks of all time.

Early years

Brady was born near San Francisco in San Mateo, California to Tom Sr. and Galynn. He was raised in a Irish American Catholic family of exceptionally gifted athletes. Brady regularly attended 49ers games in the 1980s, where he became a fan of quarterback Joe Montana; since then, Brady has mentioned Montana as one of his inspirations and an idol. Brady Sr. mentioned that they were in the endzone with Brady when "The Catch" was made by Dwight Clark.

Brady graduated from Junípero Serra High School in San Mateo, California.

Brady was also drafted as a catcher in the 18th round of the 1995 MLB Draft by the Montreal Expos.

College career

Brady played college football for, and graduated from, the University of Michigan. He was a backup his first two years, while teammate and future NFL quarterback Brian Griese led the Wolverines to a share of the national championship in 1997 in the Rose Bowl. When he enrolled at Michigan, Brady was seventh on the depth chart and had an intense struggle to get some playing time. At one point, Brady hired a sports psychologist to help him cope with frustration and anxiety and even considered transferring to Cal. Brady battled for the starting job with Drew Henson, ultimately starting every game in the 1998 and 1999 seasons under Michigan head coach Lloyd Carr. During his first full year as starter, he set Michigan records for most pass attempts and completions in a season (214). Brady was All-Big Ten (honorable mention) both seasons and team captain his senior year. The Wolverines won 20 of 25 games when he started and shared the Big Ten Conference title in 1998. Brady capped that season with a win over Arkansas in the Citrus Bowl. In the 1999 season, Brady led Michigan to an overtime win in the Orange Bowl over Alabama, throwing for 369 yards and four touchdowns.

Professional career

2000 season

Brady was selected with pick #199, a compensatory pick, in the sixth round of the 2000 NFL Draft. According to Michael Holley's book ''Patriot Reign'', the Patriots were considering Brady and Tim Rattay, both of whom had received positive reviews from then-quarterbacks coach Dick Rehbein. Ultimately, the Patriots front office chose Brady. Ironically, even though the Patriots drafted a future superstar in the next to last round, the class of 2000 was a mediocre vintage for quarterbacks: aside from Brady, only Chad Pennington developed into a first-rate pro quarterback as well as Pro Bowler Marc Bulger.

The Patriots made the unusual decision to carry four quarterbacks (instead of three) on the roster. Brady started the season as the fourth string quarterback, behind starter Drew Bledsoe and backups John Friesz and Michael Bishop; by season's end, he was number two on the depth chart behind Bledsoe. During his rookie season, he was 1-of-3 passing, for six yards.

2001 season

The Patriots opened the season with a 23–17 loss at Cincinnati, with Bledsoe as the starting quarterback. Their second game, and home opener, on September 23, was against their AFC East rival, the New York Jets. Bledsoe was again the starter, when in the fourth quarter he suffered internal bleeding after a hit from Jets linebacker Mo Lewis. Bledsoe returned for the next series, but was replaced with Brady for that Pats' final series of the game. New York would hold on to win, 10–3, and the Patriots fell to 0–2 on the season.

Brady was named the starter for the season's third game, against the Indianapolis Colts. In his first two games as starter, Brady posted unspectacular passer ratings of 79.6 and 58.7, respectively, in a 44–13 victory over the Colts (in their last season in the AFC East) and a 30–10 loss to the Miami Dolphins.

In the Pats' fifth game, Brady began to find his stride. Trailing the visiting San Diego Chargers 26–16 in the fourth quarter, Brady led the Patriots on two scoring drives to force overtime, and another in overtime to set up a winning field goal. Brady finished the game with 33 pass completions on 54 attempts, for 364 yards, and two touchdowns. The following week, Brady again played well during the rematch at Indianapolis, with a passer rating of 148.3 in a 38–17 win. The Patriots went on to win 11 of the 14 games Brady started, and six straight to finish the regular season, winning the AFC East and entering the playoffs with a first-round bye. Brady finished with 2,843 passing yards and 18 touchdowns and earned an invitation to the Pro Bowl.

In Brady's first playoff game, against the Oakland Raiders, he threw for 312 yards and led the Patriots back from a ten-point fourth-quarter deficit to send the game to overtime, where they won on an Adam Vinatieri field goal. A controversial play in that game came when, trailing by three in the fourth quarter, Brady lost control of the ball after being hit by fellow Wolverine Charles Woodson. Oakland initially recovered the ball, but, citing the "tuck rule," which states that any forward throwing motion by a quarterback begins a pass even if the quarterback loses possession of the ball as he is attempting to tuck it back toward his body, referee Walt Coleman overturned the call on instant replay, ruling it an incomplete pass rather than a fumble.

In the AFC Championship Game against the Pittsburgh Steelers, Brady injured his knee, and was relieved by Bledsoe. The Patriots won the game and were immediately instituted by Las Vegas oddsmakers as 14-point underdogs against the NFC champion St. Louis Rams in Super Bowl XXXVI.

The score was tied with 1:21 left in the Super Bowl and the Patriots were at their own 15—with no timeouts—when sportscaster and Super Bowl-winning coach John Madden said he thought the Patriots should run out the clock and try to win the game in overtime. Instead, Brady drove the Patriots' offense down the field to the Rams 31 before spiking the ball with seven seconds left. The Patriots won the game on another Adam Vinatieri field goal as time expired. Brady was named MVP of Super Bowl XXXVI while throwing for 145 yards, one touchdown, and no interceptions, becoming the then-youngest quarterback to ever win a Super Bowl.

2002 season

Brady and the Patriots finished the year at 9–7, tied with the New York Jets and Miami Dolphins for the best record in the division; however, the Jets won the division on the third tiebreaker, and the Patriots missed the playoffs.

Although posting a career-low single-season rating of 85.7, Brady threw for a league-leading 28 touchdown passes and 921 more yards than in 2001, though his fourteen interceptions would turn out to be a career high. However, Brady played much of the second half of the season with a shoulder injury, and New England head coach Bill Belichick has since indicated that if the Patriots had made the playoffs, Brady would not have been able to play in the first game due to that injury.

2003 season

In the 2003 NFL season, after a 2–2 start, Brady led the Patriots to twelve consecutive victories to finish the season, thus winning the AFC East. Statistically, Brady's strongest game of the season was against Buffalo, when he achieved a season-high quarterback rating of 122.9. Brady finished with 3,620 passing yards and 23 touchdowns, and was second in NFL MVP voting to rival Peyton Manning and Steve McNair. In the first two rounds of the playoffs, the Patriots defeated the Tennessee Titans and Indianapolis Colts. On February 1, 2004, Brady led the Patriots to a 32–29 victory over the NFC champion Carolina Panthers in Super Bowl XXXVIII and was named Super Bowl MVP for the second time. During the game, Brady threw for 354 yards with three touchdowns and set the record for most completions by a QB in a Super Bowl (32). With 1:08 left in the fourth quarter and the score tied 29–29, Brady engineered a drive to put the Patriots in position for the game-winning field goal.

2004 season

During the 2004 season, Brady helped the Patriots set an NFL record with 21 straight wins dating from the previous year, an accomplishment honored in the Pro Football Hall of Fame (though for official records, the NFL considers it an 18-game regular season winning streak; it does not count playoff games). New England's 14–2 record equalled that of their 2003 season, as well as the best regular-season record ever for a defending champion. The Patriots also won the AFC East divisional title for the third time in four years. Brady threw for 3,692 yards and 28 touchdowns, with a 92.6 passer rating, and was voted to his second Pro Bowl. In the AFC playoffs, Brady led the Patriots to victories over the Indianapolis Colts and the Pittsburgh Steelers. Brady played his best game of the year in Pittsburgh despite requiring intravenous treatment the previous night when he ran a temperature of 103 degrees. Against the NFL's best defensive team, Brady recorded a quarterback passer rating of 130.5, his highest of the season. On February 6, 2005, the Brady-led Patriots defeated the Philadelphia Eagles to win Super Bowl XXXIX. Brady threw for 236 yards and two touchdowns, most of which went to Deion Branch, while capturing the Patriots' third championship in four years.

2005 season

During the 2005 season, the Patriots were forced to rely more on Tom Brady's passing, due to injuries suffered by running backs Corey Dillon, Patrick Pass, and Kevin Faulk. Brady also had to adjust to a new center and a new running back: Heath Evans. The results were positive; Brady finished first in the league with 4,110 passing yards and third in the league with 26 touchdowns. At 92.3, his 2005 passer rating was the second-highest of his career at the time, although he equalled his career high for interceptions with fourteen. He also rushed for 89 yards and fumbled a career-low four times. Brady and the Patriots finished with a 10–6 record, winning their third straight AFC East title. Some of the highlights of the season included another game with the Steelers, in which Brady helped lead the team on the game-winning drive. When the Patriots visited the Atlanta Falcons, Brady achieved a regular season-high rating of 140.3.

In the playoffs, Brady led the Patriots to a 28–3 victory over the Jacksonville Jaguars in the wild card round; however, on January 14, 2006, the Patriots lost 27–13 to the Denver Broncos at INVESCO Field. Brady threw for 346 yards in the game with one touchdown and two interceptions, in the first playoff loss of his career. After the season's end, it was revealed that Brady had been playing with a sports hernia since December. Linebacker Willie McGinest commented on it and said he knew, but Brady continued on playing. This is the main reason Brady did not go to the Pro Bowl when he was invited.

Despite not playing in the game, Brady was present at Super Bowl XL, as the official coin tosser and as part of a celebration of Super Bowl MVP Award winners.

2006 season

Brady led the Patriots to a 12–4 record and the fourth seed in the AFC playoffs despite having an almost completely new receiving corps. In the regular season, Brady threw for 3,529 yards and 24 touchdowns. He was not among the players initially selected to the Pro Bowl, although he was offered an injury-replacement selection when Philip Rivers was forced to withdraw (which he declined).

In the postseason, the Patriots first hosted their division rivals, the New York Jets, in the wild-card round. The Patriots defeated the Jets 37–16, as Brady went 22–34 for 212 yards and two TDs. In the divisional round, the Patriots traveled to San Diego to take on the Chargers. This was Brady's first playoff game in his home state of California. Brady and the Patriots struggled against the Chargers, whom many had picked as favorites to win Super Bowl XLI. With eight minutes left in the fourth quarter and the Patriots down by eight points, Brady and the Patriots started a key drive that would ultimately decide the game. After a 49-yard pass play to Reche Caldwell, a Stephen Gostkowski field goal gave the Patriots a 24–21 win.

In the AFC championship, the Patriots faced the Indianapolis Colts. The Patriots and Colts had faced each other twice in the previous three postseasons at Foxboro; this game, however, was played at Indianapolis. The Patriots led at halftime, 21–6; however, the Colts staged a comeback, resulting in a last minute interception thrown by Brady, and a Patriots loss.

2007 season

Playing with a dramatically overhauled receiver corps—in the 2007 offseason, the Patriots acquired wide receivers Donté Stallworth, Wes Welker, Kelley Washington and Randy Moss; tight end Kyle Brady; and running back Sammy Morris—Brady enjoyed what some sports writers have described as the best season ever by a quarterback. Brady, along with Moss, decided to withdraw from the 2008 Pro Bowl. The average score of a 2007 Patriots regular season game would be 37–17 by the end of the year. Brady not only led the Patriots to a 16–0 record, outscoring opponents by more than a 2-to-1 margin, but attained numerous career, franchise, and NFL records and milestones:

Week 6: Visiting Dallas, he had a career-high five passing touchdowns in a 48–27 win. The win tied him with Roger Staubach for the most wins ever by a starting quarterback in his first 100 regular-season games, with 76. Week 7: In a 49–28 win at Miami, he had yet another record day, with six passing touchdowns, setting a franchise record. He also had the first perfect passer rating of his career.

Week 8: In a 52–7 rout at home against Washington, he threw three touchdowns, giving him a career-best 30 for the season; his previous best was 28—in an entire season—in 2002 and 2004. The win also gave Brady a victory over every NFL franchise except New England.

Week 9: In a come-from-behind 24–20 victory at Indianapolis, he threw for another three touchdowns, for a total of 33 on the season; his 32nd touchdown of the season, to Wes Welker, broke Babe Parilli's Patriots record of 31 touchdowns in a season—in five fewer games. It was also the ninth consecutive game in which he had thrown three or more touchdowns, breaking Peyton Manning's NFL record of eight.

Week 11: Following the Patriots' bye week, Brady threw for another five touchdown passes in a 56–10 rout of Buffalo, breaking Steve Grogan's franchise record for career touchdown passes with 185.

Week 12: In a 31–28 win over Philadelphia, he only threw for a single touchdown, ending his streak of three-touchdown games at ten, but reached 25,000 regular-season passing yards.

Week 13: In another come-from-behind win, a 27–24 win against the Baltimore Ravens, he became the fourth quarterback—after Kurt Warner, Peyton Manning, and Dan Marino (who did it twice)—to throw 40 touchdown passes in a season.

Week 14: In a 34–13 victory against Pittsburgh, he threw four touchdowns, putting him third all-time for touchdown passes in a single season with 45, behind Peyton Manning in 2004 and Marino in 1984. It was his eleventh game with at least three touchdown passes, beating Marino's 1984 record of ten. He also reached the 4,000 yards passing mark for the second time in his career.

Week 15: Brady, making his 108th consecutive regular-season start at quarterback, surpassed Joe Ferguson for the fourth-longest streak in NFL history, after Brett Favre, Peyton Manning, and Ron Jaworski.

Week 16: Brady's third touchdown of the day was the Patriots' 71st total touchdown of the season, breaking the NFL record of 70 set by the Miami Dolphins in 1984. This was his twelfth game of the season with three or more touchdown passes, extending his own NFL record. This was also the Patriots', and Brady's, 18th consecutive regular-season win, tying the NFL record they set in 2003 and 2004.

Week 17: Brady threw two touchdown passes; his second touchdown was his 50th, breaking Peyton Manning's 2004 record of 49. The pass was also Randy Moss' 23rd touchdown catch of the season, breaking Jerry Rice's record of 22 in a season. The win finished off the first 16–0 season in NFL history, and was the Patriots' 19th consecutive regular season win, breaking their own 2003–2004 league record of 18. Brady finished 398/578 for 4,806 yards (#3 all-time) and 50 touchdowns (#1 all time) versus only eight interceptions, and a 117.2 passer rating (#2 all-time). His 398 completions were fifth all-time. Brady was named the NFL MVP for this season, as well as Offensive Player of the Year.

2007 playoffs

In the Patriots' first playoff game, an AFC Divisional game against Jacksonville, Brady began the game with an NFL postseason record sixteen consecutive completed passes, and finished the game with 26 completions in 28 attempts, a completion rate of 92.9%. That mark is the highest single-game completion percentage (for passers with at least 20 attempts) in NFL history, regular season or postseason. With the win, the Patriots matched the Dolphins as the only team to win 17 consecutive games in one season.

Statistically, Brady did not fare as well in the AFC Championship Game against the San Diego Chargers, throwing three interceptions (including his first interception in the red zone since the playoff loss to Denver). Nevertheless, the Patriots won their 18th game of the season, 21–12, to advance to the Super Bowl for the fourth time in seven seasons. Brady, with the 100th win of his career, also set an NFL record for the fewest games needed by a starting quarterback to do so: his 100–26 record is sixteen games better than Joe Montana's. In Super Bowl XLII, Brady was pressured heavily and sacked five times. The Patriots did manage to take the lead with a Brady touchdown to Moss with less than three minutes remaining in the fourth quarter, but the Giants were able to score a last-minute touchdown to upset the Patriots 17–14.

Awards

Brady won numerous NFL awards during the season: he was voted FedEx Express NFL Player of the Week (an award for quarterbacks) four times (in Weeks 6, 7, 11, and 17), selected as AFC Offensive Player of the Week five times (in Weeks 3, 6, 7, 14, and 17), and AFC Offensive Player of the Month for both September and October. On 2008-01-05, Brady was named the NFL MVP, garnering a record-tying 49 of 50 possible votes (the other vote went to Brett Favre), making him the first Patriot to ever win the award. He was also named NFL Offensive Player of the Year in 2007 and 2010.

2008 season

Brady did not play any of the 2008 preseason due to a right foot injury from the previous AFC Championship game. In the Patriots' 2008 season opener against the Kansas City Chiefs at Gillette Stadium, Brady's left knee was seriously injured midway through the first quarter on a hit by Chiefs safety Bernard Pollard; he left the game and did not return. The team later confirmed that Brady would need surgery, and that he had been placed on injured reserve for the remainder of the season. It is believed he tore both his anterior cruciate ligament and his medial collateral ligament. The injury ended Brady's streak of 111 consecutive starts (fourth in the list of most consecutive starts by an NFL quarterback, behind Brett Favre, Peyton Manning, and Ron Jaworski). Dr. Neal ElAttrache performed the anterior cruciate ligament reconstruction at the Los Angeles Kerlan-Jobe Orthopaedic Clinic October 6, using Brady's patellar tendon graft to replace the torn ligament, and also repaired his medial collateral ligament, through a separate incision in his left knee. An infection in the wound resulted in further debridement surgery several times since the original procedure. Brady underwent IV antibiotics for this infection which, at the time, threatened to delay his rehab.

2009 season

In his first official game back from injury, Brady threw for 378 yards and two touchdowns in the 2009 season opener against the Buffalo Bills. In the final minutes of the game, the Patriots were down 24–13 before Brady and Benjamin Watson connected on two straight touchdowns to lead the Patriots to a 25–24 win. Brady was named the AFC Offensive Player of the Week for the 13th time in his career for his performance.

On October 18, 2009, in an early season snowstorm, Brady set an NFL record against the Tennessee Titans for most touchdowns in a single quarter, throwing five (two to Moss, one to Faulk, and two to Welker) in the second quarter. Brady finished the game with six touchdowns, tying his career best, and 380 yards, completing 29 of 34 attempts, finishing with a nearly perfect passer rating of 152.8. The Patriots' 59–0 victory over the Titans tied the record for the largest margin of victory since the 1970 AFL-NFL merger, and set a record for largest halftime lead in NFL history (they led 45–0). He was named AFC Offensive Player of the Week again for his performance. In Week 16, Brady set a Patriots regular season record with an 88.5% completion percentage against the Jacksonville Jaguars; he was named AFC Offensive Player of the Week after the game.

Brady would finish the 2009 regular season with 4,398 yards passing and 28 touchdowns for a 96.2 rating, despite a broken right ring finger and three fractured ribs, all which were suffered over the course of the season. He was selected as a reserve to the 2010 Pro Bowl and named the 2009 NFL Comeback Player of the Year.

Brady ended the 2009 season throwing 3 interceptions in a Wild Card playoff loss to the Baltimore Ravens, 33–14, his first career home playoff loss, and the first playoff loss at home by a New England Patriots quarterback since 1978.

2010 season – Second MVP

On September 10, 2010, Brady signed a four-year, $72 million contract extension making him the highest-paid player in the NFL. The extension includes $48.5 million in guaranteed money and will likely keep Brady with the Patriots through the 2014 NFL season. The news of the contract occurred on the same day Brady escaped uninjured from a 6:30 a.m. car accident with what the ''Boston Herald'' called, "a road scofflaw".

Brady became the quickest to achieve 100 regular season wins by helping his team defeat the Miami Dolphins 41–14 on October 4, 2010.

On November 21, 2010, Brady tied Brett Favre's record of winning 25 consecutive regular-season home starts, in a 31–28 win over the Indianapolis Colts. Brady's last regular-season loss at home was on November 12, 2006, a 17–14 loss to the New York Jets. On December 6, 2010, Brady set an NFL record by winning 26 consecutive regular-season home starts, in a 45–3 victory over the New York Jets.

On December 19, 2010, in a 31–27 home win over the Green Bay Packers, Brady had his seventh straight two-touchdown game without an interception, surpassing Don Meredith's NFL record of six such games. The next week in a 34–3 road win over the Buffalo Bills, Brady surpassed Bernie Kosar's 1990–1991 record of 308 consecutive pass attempts without an interception.

Brady's 9:1 touchdown-to-interception ratio (36:4) would break his own single-season record of 6.25:1, which he set in 2007. No other qualifying quarterback in NFL history has had a 6:1 touchdown-to-interception ratio for a season. Brady threw for 3,900 yards with 36 touchdowns and just four interceptions. He had an 111.0 passer rating, giving him two of the top five season ratings in NFL history, and making him the first player to finish with a rating above 110 in two different seasons.

Brady was selected as a starter to the 2011 Pro Bowl. However, he pulled out of the game (and was replaced by former backup Matt Cassel of the Kansas City Chiefs) after undergoing surgery for a stress fracture in his right foot dating back to 2008. Brady was also the only unanimous selection for the AP All-Pro Team and was named the 2010 Associated Press NFL Offensive Player of the Year. He also achieved by unanimous decision the MVP award for the second time in his career.

Statistics

Regular season

3 !2001 NFL season 413 !2002 NFL season 601 !2003 NFL season 527 !2004 NFL season 474 !2005 NFL season 530 !2006 NFL season 516 !2007 NFL season 578 !2008 NFL season 11 !2009 NFL season 565 !2010 NFL season 492

rowspan="2"	Year !! rowspan="2"|Team !! rowspan="2"|G !! rowspan="2"|GS !! colspan="8" |Passing !! colspan="4" |Rushing !! colspan="2" |Sacked !! colspan="2" |Fumbles
! Att !! Comp !! Pct !! Yds !! Y/A !! TD !! Int !! Rtg !! Att !! Yds !! Avg !! TD !! Sack !! Yds !! Fum !! Lost
![[2000 NFL season	1	0	|	1	33.3	6	2.0	0	0	42.4	0	0	0	0	0	0	0	0
2001 !	NE	15	14	|	264	63.9	2,843	6.9	18	12	86.5	36	43	1.2	0	41	216	12	3
2002 !	NE	16	16	|	373	62.1	3,764	6.3	28	14	85.7	42	110	2.6	1	31	190	11	5
2003 !	NE	16	16	|	317	60.2	3,620	6.9	23	12	85.9	42	63	1.5	1	32	219	13	5
2004 !	NE	16	16	|	288	60.8	3,692	7.8	28	14	92.6	43	28	0.7	0	26	162	7	5
2005 !	NE	16	16	|	334	63.0	4,110	7.8	26	14	92.3	27	89	3.3	1	26	188	4	3
2006 !	NE	16	16	|	319	61.8	3,529	6.8	24	12	87.9	49	102	2.1	0	26	175	12	4
2007 !	NE	16	16	|	398	68.9	4,806	8.3	50	8	117.2	37	98	2.6	2	21	128	6	4
2008 !	NE	1	1	|	7	63.6	76	6.9	0	0	83.9	0	0	0	0	0	0	0	0
2009 !	NE	16	16	|	371	65.7	4,398	7.8	28	13	96.2	29	44	1.5	1	16	86	4	2
2010 !	NE	16	16	|	324	65.9	3,900	7.9	36	4	111.0	31	30	1.0	1	25	175	3	1
Total !! 145 !! 143 !! 4,710 !! 2,996 !! 63.6 !! 34,744 !! 7.4 !! 261 !! 103 !! 95.2 !! 336 !! 607 !! 1.8 !! 7 !! 244 !! 1,539 !! 72 !! 32

Playoffs

97 !2003–04 NFL playoffs 126 !2004–05 NFL playoffs 81 !2005–06 NFL playoffs 63 !2006–07 NFL playoffs 119 !2007–08 NFL playoffs 109 !2009–10 NFL playoffs 42 !2010–11 NFL playoffs 45

rowspan="2"	Year !! rowspan="2"|Team !! rowspan="2"|G !! rowspan="2"|GS !! colspan="8" |Passing !! colspan="4" |Rushing !! colspan="2" |Sacked !! colspan="2" |Fumbles
! Att !! Comp !! Pct !! Yds !! Y/A !! TD !! Int !! Rtg !! Att !! Yds !! Avg !! TD !! Sack !! Yds !! Fum !! Lost
![[2001–02 NFL playoffs	3	3	|	60	61.9	572	5.9	1	1	77.3	8	22	2.8	1	5	36	1	0
2003 !	NE	3	3	|	75	59.5	792	6.3	5	2	84.5	12	18	1.5	0	0	0	0	0
2004 !	NE	3	3	|	55	67.9	587	7.2	5	0	109.4	7	3	0.4	1	0	0	1	1
2005 !	NE	2	2	|	35	55.6	542	8.6	4	2	92.2	3	8	2.7	0	4	12	2	0
2006 !	NE	3	3	|	70	58.8	724	6.1	5	4	76.5	8	18	2.2	0	4	22	2	0
2007 !	NE	3	3	|	77	70.6	737	6.8	6	3	96.0	4	−1	−0.2	0	8	52	1	1
2009 !	NE	1	1	|	23	54.8	154	3.7	2	3	49.1	0	0	0	0	3	22	1	1
2010 !	NE	1	1	|	29	64.4	299	6.6	2	1	89.0	2	2	1.0	0	5	40	1	0
Total !! 19 !! 19 !! 682 !! 424 !! 62.2 !! 4,407 !! 6.5 !! 30 !! 16 !! 85.7 !! 44 !! 70 !! 1.6 !! 2 !! 29 !! 184 !! 9 !! 3

Personal life

Brady dated actress Bridget Moynahan from 2004 until late 2006. On February 18, 2007, Moynahan confirmed to ''People'' magazine that she was more than three months pregnant with her and Brady's child. Brady and Moynahan ended their relationship sometime in early December 2006, around the time Moynahan became pregnant. Brady was present when the baby, John Edward Thomas Moynahan, was born on August 22, 2007 at Saint John's Health Center in Santa Monica. The baby has Brady's first and middle names as middle names, though in reverse order (Moynahan's father's first name is Edward, however).

Brady married Brazilian supermodel Gisele Bündchen on February 26, 2009 in an intimate Catholic ceremony in Santa Monica, California. On June 19, 2009, reports surfaced that Bündchen was pregnant. On September 11, 2009, Brady confirmed to ESPN that they were indeed expecting, and that Bündchen was due in December 2009. On December 8, 2009, Bündchen gave birth to the couple's first child together, a son. On December 18, 2009, Bündchen posted a message on her website indicating that their son's name is Benjamin. In the April 2010 issue of ''Vogue'' magazine, Bündchen confirmed that his name is Benjamin Rein Brady and that his middle name is a shortened version of her father's name Reinoldo. They christened their 6-month-old son Benjamin in Santa Monica on June 22, 2010.

Two paparazzi photographers claim they were shot at by security guards after Brady and Bundchen renewed their wedding vows in Costa Rica on April 5, 2009. Photographs appeared in the ''Boston Herald'' of the shattered rear window of a vehicle belonging to one of these two paparazzi. The photographers, Yuri Cortez and Rolando Aviles, filed a lawsuit in New York against Brady and Bündchen seeking over $1 million in damages over the incident.

Notable accomplishments

NFL records

Wins

Fewest starts to achieve 100 regular-season wins as a starter (131 starts)

Most consecutive wins, postseason: 10 (2001, 2003, 2004, 2005)

Most consecutive wins, regular season and postseason: 21 (2003–2004)

Most consecutive wins in regular-season home games: 28 (2006–''present'')

Most seasons finishing 8–0 at home: 5 (2003, 2004, 2007, 2009, 2010)

Only quarterback to start and win 3 Super Bowls before his 28th birthday

Touchdowns

Most passing touchdowns, regular season: 50 (2007)

Most passing touchdowns, regular season and postseason combined: 56 (2007)

Most touchdown passes, month: 20 (October 2007)

Most passing touchdowns, quarter: 5 (second quarter vs. Tennessee, October 18, 2009)

Largest touchdown to interception differential: +42 (2007)

Highest touchdown to interception ratio, season: 9.0 to 1 (36 TD/4 INT, 2010)

Highest touchdown pass–interception ratio, career: 2.52-1 (260 TD/103 INT)

Most games with 3+ touchdown passes, regular season: 12 (2007)

Most consecutive games with 3+ touchdown passes, regular season: 10 (2007)

Most consecutive games with 2+ touchdown passes and no interceptions: 9 (2010, October 24–''present''

Most games with 1 touchdown pass and no interceptions, season: 14 (2010)

Most games with 2 touchdown passes and no interceptions, season: 11 (2010)

Most games with 3 touchdown passes and no interceptions, season: 8 (2007)

Most games with 4 touchdown passes and no interceptions, season: 5 (2007)

Most games with 4 touchdown passes and no interceptions, career: 12 – tied with Brett Favre

Most games with 5 touchdown passes and no interceptions, season: 3 (2007)

Most games with 5 touchdown passes and no interceptions, career: 4 – tied with Peyton Manning

Most games with 6 touchdown passes and no interceptions, career 2 – tied with Peyton Manning

Completions Highest single-game completion percentage, postseason: 92.9% (vs. Jacksonville, January 12, 2008)

Tied for most completions in a Super Bowl: 32 (XXXVIII)

Most career Super Bowl completions: 100 (XXXVI, XXXVIII, XXXIX, XLII)

Largest completion–interception ratio, season: 81.0-1 (324-4) (mininimum 150 completions), 2010

Most games with 20 completions and no interceptions, season: 10 (2007)

Most games with 30 completions and no interceptions, career: 9 – tied with Drew Brees

Most games with 30 completions and no interceptions, season: 5 (2007)

Most games with 50 pass attempts and no interceptions, career: 3

Yards

Largest passing yards–interception ratio, career: 337.3-1 (34,744-103) (mininimum 20,000 passing yards)

Largest passing yards–interception ratio, season: 975.0-1 (3,900-4) (mininimum 2,000 passing yards), 2010

Most games with 300 yards passing and no interceptions, season: 8 (2007)

Interception-free streaks and interception percentage

Most consecutive pass attempts to start a career without an interception: 162 (2000–2001)

Most consecutive pass attempts without an interception, regular season: 338 (2010, October 24–''present'')

Third-lowest interception percentage (interceptions per attempt), career: 2.19% (Aaron Rodgers ranks first @ 1.99%; Neil O'Donnell is second @ 2.11%)

Career bests

Excluding the list of NFL records above:

Highest single-game quarterback rating: 158.3 (at Miami, October 21, 2007 and at Detroit, November 25, 2010) Perfect Rating

Highest single-season quarterback rating: 117.2 (2007) 2nd highest all-time

Most passing touchdowns, game: 6 (at Miami, October 21, 2007 and vs. Tennessee, October 18, 2009)

Most passing yards, game: 410 (vs. Kansas City, 2002)

Most passing yards, season: 4,806 (2007)

Lowest interception total, season (minimum 2 starts): 4 (2010)

21-game win streak statistics (including post-season)

690 passes attempted

412 passes completed

4,953 passing yards

34 passing touchdowns

13 passes intercepted

20.29 passing attempts per touchdown

53.07 passing attempts per interception

59.71 completion rate

90.3 passer rating

Career

111–32 (regular season), 125–37 (career) as a starter

8–1 (career) in overtime games

34–6 (career) vs. NFC teams

32 game-winning drives after a Patriots' fourth-quarter tie or deficit

Post-season records and statistics

NFL record for most consecutive wins in post season: 10 (broke record of Green Bay's Bart Starr).

Most consecutive post season wins (college and professional combined): 12

3 Super Bowl victories

2 Super Bowl MVP awards

Most completions in a Super Bowl (32 in Super Bowl XXXVIII)

Most career Super Bowl completions (100 in four games)

Highest completion percentage in a single game, minimum 20 attempts (26 of 28, 92.9%, against Jacksonville in 2007 AFC Divisional round)

See also

Most wins by a starting quarterback (NFL)

Most consecutive starts by a quarterback (NFL)

Most career 300-yard passing games by NFL quarterbacks

List of NFL quarterbacks who have passed for 400 or more yards in a game

List of NFL starting quarterback playoff records

List of NFL quarterbacks who have posted a perfect passer rating

Lists of Michigan Wolverines football passing leaders

Saturday Night Live hosts

2005 ''Simpsons'' episode "Homer and Ned's Hail Mary Pass"

2006 ''Family Guy'' episode "Patriot Games"

References

Further reading

External links

Tom Brady's official website

Tom Brady biography on the New England Patriots' official website

Category:1977 births Category:Living people Category:American Conference Pro Bowl players Category:American football quarterbacks Category:American Roman Catholics Category:American people of Irish descent Category:Michigan Wolverines football players Category:New England Patriots players Category:People from San Mateo, California Category:Players of American football from California Category:Super Bowl MVPs

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Coordinates	51°54′42″N04°23′58″N
Name	Tupac Amaru Shakur
Background	solo_singer
Birth name	Lesane Parish Crooks
Alias	2Pac, Pac, Makaveli
Origin	Los Angeles, California, U.S.
Born	June 16, 1971East Harlem, New York City
Died	September 13, 1996Las Vegas, Nevada, U.S.
Genre	Hip hop
Occupation	Rapper, actor, record producer, poet, screenwriter, activist, writer
Years active	1988–1996 (rapping) 1990–1996 (acting)
Label	Interscope, Death Row, Amaru
Associated acts	Outlawz, Johnny "J", Snoop Doggy Dogg, Digital Underground, Richie Rich, K-Ci & JoJo, Dave Hollister, Dr. Dre, Tha Dogg Pound, Boot Camp Clik, Nate Dogg, Young Noble
Website	}}

Tupac Amaru Shakur (June 16, 1971 – September 13, 1996), known by his stage names 2Pac (or simply Pac) and Makaveli, was an American rapper and actor. Shakur has sold over 75 million albums worldwide as of 2007, making him one of the best-selling music artists in the world. ''Rolling Stone Magazine'' named him the 86th Greatest Artist of All Time.

In addition to his career as a rap artist, he was also an actor. The themes of most of Tupac's songs are the violence and hardship in inner cities, racism, other social problems, and conflicts with other rappers during the East Coast – West Coast hip hop rivalry. Shakur began his career as a roadie and backup dancer for the alternative hip hop group Digital Underground.

On September 7, 1996, Shakur was shot four times in the Las Vegas metropolitan area of Nevada. He was taken to the University Medical Center, where he died 6 days later of respiratory failure and cardiac arrest.

Early life

Tupac Amaru Shakur was born on the East Harlem section of Manhattan in New York City. He was named after Túpac Amaru II, a Peruvian revolutionary who led an indigenous uprising against Spain and was subsequently executed.

His mother, Afeni Shakur, and his father, Billy Garland, were active members of the Black Panther Party in New York in the late 1960s and early 1970s; he was born just one month after his mother's acquittal on more than 150 charges of "Conspiracy against the United States government and New York landmarks" in the New York Panther 21 court case.

Although unconfirmed by the Shakur family, several sources (including the official coroner's report) list his birth name as "Lesane Parish Crooks". This name was supposedly entered on the birth certificate because Afeni feared her enemies would attack her son, and disguised his true identity using a different last name. She changed it later, following her separation from Garland and marriage to Mutulu Shakur.

Struggle and incarceration surrounded Shakur from an early age. His godfather, Elmer "Geronimo" Pratt, a high ranking Black Panther, was convicted of murdering a school teacher during a 1968 robbery, although his sentence was later overturned. His stepfather, Mutulu, spent four years at large on the FBI's Ten Most Wanted Fugitives list beginning in 1982. Mutulu was wanted in part for having helped his sister Assata Shakur (also known as Joanne Chesimard) to escape from a penitentiary in New Jersey, where she had been incarcerated for shooting a state trooper to death in 1973. Mutulu was caught in 1986 and imprisoned for the robbery of a Brinks armored truck in which two police officers and a guard were killed. Shakur had a half-sister, Sekyiwa, two years his junior, and an older stepbrother, Mopreme "Komani" Shakur, who appeared on many of his recordings.

At the age of twelve, Shakur enrolled in Harlem's 127th Street Repertory Ensemble and was cast as the Travis Younger character in the play ''A Raisin in the Sun'', which was performed at the Apollo Theater. In 1986, the family relocated to Baltimore, Maryland. After completing his second year at Paul Laurence Dunbar High School he transferred to the Baltimore School for the Arts, where he studied acting, poetry, jazz, and ballet. He performed in Shakespeare plays, and in the role of the Mouse King in ''The Nutcracker''. Shakur, accompanied by one of his friends, Dana "Mouse" Smith, as his beatbox, won most of the many rap competitions that he participated in and was considered to be the best rapper in his school. He was remembered as one of the most popular kids in his school because of his sense of humor, superior rapping skills, and ability to mix in with all crowds. He developed a close friendship with a young Jada Pinkett (later Jada Pinkett Smith) that lasted until his death. In the documentary ''Tupac: Resurrection'', Shakur says, "Jada is my heart. She will be my friend for my whole life," and Pinkett Smith calls him "one of my best friends. He was like a brother. It was beyond friendship for us. The type of relationship we had, you only get that once in a lifetime." A poem written by Shakur titled "Jada" appears in his book, ''The Rose That Grew From Concrete'', which also includes a poem dedicated to Pinkett Smith called "The Tears in Cupid's Eyes". During his time in art school, Shakur began dating the daughter of the director of the Baltimore Communist Party USA.

In June 1988, Shakur and his family moved to Marin City, California, where he attended Tamalpais High School. He began attending the poetry classes of Leila Steinberg in 1989. That same year, Steinberg organized a concert with a former group of Shakur's, Strictly Dope; the concert led to him being signed with Atron Gregory who set him up as a roadie and backup dancer with the young rap group Digital Underground in 1990.

Career

Rapping career

Shakur's professional entertainment career began in the early 1990s, when he debuted his rapping skills in a vocal turn in Digital Underground's "Same Song" from the soundtrack to the 1991 film ''Nothing but Trouble'' and also appeared with the group in the film of the same name. The song was later released as the lead song of the Digital Underground EP ''This is an EP Release'', the follow-up to their debut hit album ''Sex Packets''. Shakur appeared in the accompanying music video. After his rap debut, he performed with Digital Underground again on the album ''Sons of the P''. Later, he released his first solo album, ''2Pacalypse Now''.

''2Pacalypse Now'' did not do as well on the charts as future albums, spawning no top ten hits. His second record, ''Strictly 4 My N.I.G.G.A.Z.'', was released in 1993.

Thug Life

In late 1993, Shakur formed the group Thug Life with a number of his friends, including Big Syke, Macadoshis, his stepbrother Mopreme Shakur, and Rated R. The group released their only album ''Thug Life: Volume 1'' on September 26, 1994, which went gold. The album featured the single "Pour Out a Little Liquor" produced by Johnny "J" Jackson, who went on to produce a large part of Shakur's album ''All Eyez on Me''. The group usually performed their concerts without Shakur.

Influences

Shakur's music and philosophy is rooted in many American, African-American, and World entities, including the Black Panther Party, Black nationalism, egalitarianism, and liberty. His debut album, ''2Pacalypse Now'', revealed the socially conscious side of Shakur. On this album, Shakur attacked social injustice, poverty and police brutality on songs "Brenda's Got a Baby", "Trapped" and "Part Time Mutha". His style on this album was highly influenced by the social consciousness and Afrocentrism pervading hip hop in the late 1980s and early 1990s. On this initial release, Shakur helped extend the success of such rap groups as Boogie Down Productions, Public Enemy, X-Clan, and Grandmaster Flash, as he became one of the first major socially conscious rappers from the West Coast.

On his second record, Shakur continued to rap about the social ills facing African-Americans, with songs like "The Streetz R Deathrow" and "Last Wordz". He also showed his compassionate side with the anthem "Keep Ya Head Up", while simultaneously putting his legendary aggressiveness on display with the title track from the album ''Strictly 4 My N.I.G.G.A.Z.'' he added a salute to his former group Digital Underground by including them on the playful track "I Get Around". Throughout his career, an increasingly aggressive attitude can be seen pervading Shakur's subsequent albums.

The contradictory themes of social inequality and injustice, unbridled aggression, compassion, playfulness, and hope all continued to shape Shakur's work, as witnessed with the release of his incendiary 1995 album ''Me Against the World''. In 1996, Shakur released ''All Eyez on Me''. Many of these tracks are considered by many critics to be classics, including "Ambitionz Az a Ridah", "I Ain't Mad at Cha", "California Love", "Life Goes On" and "Picture Me Rollin'".; ''All Eyez on Me'' was a change of style from his earlier works. While still containing socially conscious songs and themes, Shakur's album was heavily influenced by party tracks and tended to have a more "feel good" vibe than his first albums. Shakur described it as a celebration of life, and the record was critically and commercially successful.

Personal life

Shakur was a voracious reader. He was inspired by a wide variety of writers, including William Shakespeare, Niccolò Machiavelli, Donald Goines, Sun Tzu, Kurt Vonnegut, Mikhail Bakunin, Maya Angelou, Alice Walker, and Khalil Gibran. In his book, Dyson describes the experience of visiting the home of Shakur's friend and promoter Leila Steinberg to find "the sea of books" once owned by Shakur.

Shakur never professed following a particular religion, but his lyrics in singles such as 'Only God Can Judge Me' and poems such as ''The Rose That Grew from Concrete'' suggests he believed in God. This means many analysts currently describe him as a deist. He believed in Karma, but rejected a literal afterlife and organized religion.

Legal issues

Even as he garnered attention as a rapper and actor, Shakur gained notoriety for his conflicts with the law:

In October 1991, he filed a $10 million civil suit against the law enforcement of the Oakland Police Department, alleging they brutally beat him for jaywalking.

In 1992, a Texas state trooper was killed by a teenager who was listening to ''2Pacalypse Now'' which included songs about killing police. This caused a swirl of media controversy. Dan Quayle, the Vice President of the United States at the time, demanded that the album be withdrawn from music stores and media across the country; Interscope refused. Shakur claimed his first album was aimed at the problems facing young black males, but it was criticized for its graphic language and images of violence by and against law enforcement. Quayle publicly denounced the album as having "no place in our society."

On August 22, 1992, in Marin City, California, Shakur rapped at an outdoor festival, and stayed for an hour signing autographs and pictures. Some earlier negative remarks made by Shakur about Marin City had caught up and when arguments started, voices got loud; he pulled a Colt Mustang, cocked it, fumbled and it fell. Someone picked up the gun and a bullet discharged. Though nobody in the crowd was shot, about 100 yards away, 6-year-old Qa'id Walker-Teal rode a bicycle at a schoolyard and was hit in the forehead with a bullet that killed him. (Some sources reported that the child was the victim of a stray bullet in a shootout between Shakur's entourage and a rival group.) Shakur and Mopreme left in their car and were stopped by an angry mob, by chance, in front of a sheriff's substation. The police "rescued" them and took the two into custody, who were soon released without charge. In 1995, a wrongful death suit was brought against Shakur by Qa'id's mother. Ballistics tests proved the bullet that killed the boy was not from Shakur's or any members of his entourage's guns. No criminal charges were brought. Shakur's lawyer said that the festival was a "nasty situation," and Shakur was saddened by the death of the boy. Shakur's record company settled the lawsuit for an undisclosed amount, reportedly between $300,000 and $500,000.

In October 1993, in Atlanta, two brothers and off-duty police officers, Mark and Scott Whitwell, were with their wives celebrating Mrs. Whitwell's recent passing of the state bar examination. As they crossed the street, a car with Shakur inside passed by them or "almost struck them," after which the Whitwells began an altercation with the driver, Shakur and the other passengers, which was then joined by a second passing car. Shakur shot one officer in the buttocks, and the other in the leg, back, or abdomen, according to varying news reports. There were no other injuries, but Mark Whitwell was charged with firing at Shakur's car and later lying to the police during the investigation, and Shakur with the shooting, until prosecutors decided to drop all charges against all parties.

In November 1993, Shakur and others were charged with sexually assaulting a woman in a hotel room. According to the complaint, Shakur sodomized the woman and then encouraged his friends to sexually abuse her. Shakur denied the charges. According to Shakur, he had prior relations days earlier with the woman; she performed oral sex on him on a club dance floor and the two later had consensual sex in his hotel room. The complainant claimed sexual assault after her second visit to Shakur's hotel room; she alleged that Shakur and his entourage gang banged her, and she said to Shakur when she left, "Why you let them do this to me?" Shakur claimed that he fell asleep shortly after the woman arrived and later awoke to her accusations and legal threats. In the ensuing trial, Shakur was convicted of sexual abuse. In sentencing Shakur to 1½–4½ years in prison, the judge described the crime as "an act of brutal violence against a helpless woman." After serving part of his sentence, Shakur was released on bail pending appeal. On April 5, 1996, a judge sentenced him to serve 120 days in jail for violating terms of his release on bail.

November 1994 shooting

On the night of November 30, 1994, the day before the verdict in his sexual abuse trial was to be announced, Shakur was shot five times and robbed after entering the lobby of Quad Recording Studios in Manhattan by two armed men in army fatigues. He would later accuse Sean Combs, Andre Harrell, and Biggie Smalls—whom he saw after the shooting—of setting him up. Shakur also suspected his close friend and associate, Randy "Stretch" Walker, of being involved in the attempt. According to the doctors at Bellevue Hospital, where he was admitted immediately following the incident, Shakur had received five bullet wounds; twice in the head, twice in the groin and once through the arm and thigh. He checked out of the hospital, against doctor's orders, three hours after surgery. In the day that followed, Shakur entered the courthouse in a wheelchair and was found guilty of three counts of molestation, but innocent of six others, including sodomy. On February 6, 1995, he was sentenced to one-and-a-half to four-and-a-half years in prison on a sexual assault charge.

A year later on November 30, 1995, Stretch was killed after being shot twice in the back by three men who pulled up alongside his green minivan at 112th Ave. and 209th St. in Queens Village, while he was driving. His minivan smashed into a tree and hit a parked car before flipping over.

On March 27, 2008, the ''Los Angeles Times'' issued an apology to Combs for blaming him for having a role in the November 1994 shooting. The article stated that Shakur was led to the studio by Biggie's associates to gun him down to make favor with Biggie. The newspaper relied on forged documents that The Smoking Gun proved to be faked. Combs stated that he was disgusted with the ''LA Times'' for printing the story.

On June 15, 2011, an inmate admitted to this shooting and robbery, claiming to have been hired to do so by James Rosemond, owner of Czar Entertainment.

Prison sentence

Shakur began serving his prison sentence at Clinton Correctional Facility on February 14, 1995. Shortly afterwards, he released his multi-platinum album ''Me Against the World''. Shakur became the first artist ever to have an album at number one on the Billboard 200 while serving a prison sentence: the only other artist to have achieved this feat is fellow rapper Lil Wayne, whose album ''I Am Not a Human Being'' reached number one in 2010 whilst he was serving a nine-month prison term for criminal possession of a weapon. ''Me Against the World'' made its debut on the Billboard 200 and stayed at the top of the charts for four weeks. The album sold 240,000 copies in its first week, setting a record for highest first week sales for a solo male rap artist at the time. While serving his sentence, he married his long-time girlfriend, Keisha Morris, on April 4, 1995; the couple later divorced in 1996. While imprisoned, Shakur read many books by Niccolò Machiavelli, Sun Tzu's ''The Art of War'' and other works of political philosophy and strategy. He also wrote a screenplay titled ''Live 2 Tell'' while incarcerated, a story about an adolescent who becomes a drug baron.

In October 1995, Shakur's case was on appeal but due to all of his legal fees he could not raise the $1.4 million bail. During his time in jail prisoners were telling Shakur about the illuminati. After serving eleven months of his one-and-a-half year to four-and-a-half year sentence, Shakur was released from the Attica Correctional Facility due in large part to the help and influence of Suge Knight, the CEO of Death Row Records, who posted a $1.4 million bail pending appeal of the conviction in exchange for Shakur to release three albums under the Death Row label.

Death Row Records

Upon his release from Clinton Correctional Facility, Shakur immediately went back to song recording. He began a new group called Outlaw Immortalz. Shakur began recording his first album with Death Row and released the single "California Love" soon after. On February 13, 1996, Shakur released his fourth solo album, ''All Eyez on Me''. This double album was the first and second of his three-album commitment to Death Row Records. It sold over nine million copies. The record was a general departure from the introspective subject matter of ''Me Against the World'', being more oriented toward a thug and gangsta mentality. Shakur continued his recordings despite increasing problems at the Death Row label. Dr. Dre left his post as house producer to form his own label, Aftermath. Shakur continued to produce hundreds of tracks during his time at Death Row, most of which would be released on his posthumous albums ''R U Still Down? (Remember Me)'', ''Still I Rise'', ''Until the End of Time'', ''Better Dayz'', ''Loyal to the Game'' and ''Pac's Life''. He also began the process of recording an album with the Boot Camp Clik and their label Duck Down Records, both New York–based, entitled ''One Nation''.

On June 4, 1996, he and Outlawz released the diss track "Hit 'Em Up", a scathing lyrical assault on Biggie and others associated with him. In the track, Shakur claimed to have had sexual intercourse with Faith Evans, Biggie's wife at the time, and attacks Bad Boy's street credibility. Though no hard evidence suggests so, Shakur was convinced that some members associated with Bad Boy had known about the '94 attack on him beforehand due to their behavior that night and what his sources told him. Shakur aligned himself with Suge, Death Row's CEO, who was already bitter toward Combs over a 1995 incident at the Platinum Club in Atlanta, Georgia, which culminated in the death of Suge's friend and bodyguard, Jake Robles; Suge was adamant in voicing his suspicions of Combs' involvement. Shakur's signing with Suge and Death Row added fuel to building an East Coast-West Coast conflict. Both sides remained bitter enemies until Shakur's death. On July 4, 1996, he performed live at the House of Blues with Outlawz, Tha Dogg Pound, and Snoop Doggy Dogg also headlining. This was Shakur's very last live performance.

While incarcerated in Clinton Correctional Facility, Shakur read and studied Niccolò Machiavelli and other published works, which inspired his pseudonym "Makaveli" under which he released the album ''The Don Killuminati: The 7 Day Theory''. The album presents a stark contrast to previous works. Throughout the album, Shakur continues to focus on the themes of pain and aggression, making this album one of the emotionally darker works of his career. Shakur wrote and recorded all the lyrics in only three days and the production took another four days, combining for a total of seven days to complete the album (hence the name). The album title has the word killuminati because Tupac wanted to kill the illuminati with his songs (hence the name).

Outlawz

On forming the Outlawz, Tupac gave each of them a name of a dictator/military leader or an enemy of America.

Yaki Kadafi, after Libyan dictator Muammar Gaddafi

Hussein Fatal, after Iraqi leader Saddam Hussein

Mussolini (formerly Big Syke), after Italian dictator Benito Mussolini

Komani (Shakur's half brother Mopreme), after Iranian Islamic Revolution leader Ayatollah Ruhollah Khomeini

Kastro, after Cuban leader Fidel Castro

E.D.I. Mean, after Ugandan dictator Idi Amin

Napoleon, after French strategist Napoleon Bonaparte

For himself, Tupac created the alias "Makaveli" from Renaissance Italian philosopher and strategist Niccolo Machiavelli, whose writings inspired Shakur in prison, but who also preached that a leader could eliminate his enemies by all means necessary.

He mentioned Makaveli Records a few times before his death. This was supposed to be a music label for up and coming artists that Shakur had an interest in developing or potentially signing, and his own future projects would have also been published through it as well.

September 1996 shooting and death

On the night of September 7, 1996, Shakur attended the Mike Tyson–Bruce Seldon boxing match at the MGM Grand in Las Vegas. After leaving the match, one of Suge's associates spotted 21-year-old Orlando "Baby Lane" Anderson, a member of the Southside Crips, in the MGM Grand lobby and informed Shakur, who then attacked Anderson. Shakur's entourage, as well as Suge and his followers, assisted in assaulting Anderson. The fight was captured on the hotel's video surveillance. Earlier that year, Anderson and a group of Crips had robbed a member of Death Row's entourage in a Foot Locker store, precipitating Shakur's attack. After the brawl, Shakur went to rendezvous with Suge to go to Death Row-owned Club 662 (now known as restaurant/club Seven). He rode in Suge's 1996 black BMW 750iL sedan as part of a larger convoy including many in Shakur's entourage.

At 10:55 pm, while paused at a red light, Shakur rolled down his window and a photographer took his photograph. At around 11:00–11:05 pm, they were halted on Las Vegas Blvd. by Metro bicycle police for playing the car stereo too loud and not having license plates. The plates were then found in the trunk of Suge's car; they were released without being fined a few minutes later. At about 11:10 pm, while stopped at a red light at Flamingo Road near the intersection of Koval Lane in front of the Maxim Hotel, a vehicle occupied by two women pulled up on their left side. Shakur, who was standing up through the sunroof, exchanged words with the two women, and invited them to go to Club 662. At approximately 11:15 pm, a white, four-door, late-model Cadillac with an unknown number of occupants pulled up to the sedan's right side, rolled down one of the windows, and rapidly fired a volley of gunshots at Shakur; bullets hit him in the chest, pelvis, and his right hand and thigh. One of the rounds apparently ricocheted into Shakur's right lung. Suge was hit in the head by fragmentation, though it is thought that a bullet grazed him. According to Suge, a bullet from the gunfire had been lodged in his skull, but medical reports later contradicted this statement.

At the time of the drive-by Shakur's bodyguard was following behind in a vehicle belonging to Kidada Jones, Shakur's then-fiancée. The bodyguard, Frank Alexander, stated that when he was about to ride along with the rapper in Suge's car, Shakur asked him to drive Kidada Jones' car instead just in case they were too drunk and needed additional vehicles from Club 662 back to the hotel. Shortly after the assault, the bodyguard reported in his documentary, ''Before I Wake'', that one of the convoy's cars drove off after the assailant but he never heard back from the occupants.

After arriving on the scene, police and paramedics took Suge and a mortally wounded Shakur to the University Medical Center. According to an interview with one of Shakur's closest friends the music video director Gobi, while at the hospital, he received news from a Death Row marketing employee that the shooters had called the record label and were sending death threats aimed at Shakur, claiming that they were going there to "finish him off". Upon hearing this, Gobi immediately alerted the Las Vegas police, but the police claimed they were understaffed and no one could be sent. Nonetheless, the shooters never arrived. At the hospital, Shakur was in and out of consciousness, was heavily sedated, breathed through a ventilator and respirator, was placed on life support machines, and was ultimately put under a barbiturate-induced coma after repeatedly trying to get out of the bed.

Despite having been resuscitated in a trauma center and surviving a multitude of surgeries (as well as the removal of a failed right lung), Shakur had gotten through the critical phase of the medical therapy and was given a 50% chance of pulling through. Gobi left the medical center after being informed that Shakur made a 13% recovery on the sixth night. While in the critical care unit on the afternoon of September 13, 1996, Shakur died of internal bleeding; doctors attempted to revive him but could not impede his hemorrhaging. His mother, Afeni, made the decision to tell the doctors to stop. He was pronounced dead at 4:03 pm (PDT) The official cause of death was noted as respiratory failure and cardiopulmonary arrest in connection with multiple gunshot wounds. Shakur's body was cremated and some of his ashes were later mixed with marijuana and smoked by members of the Outlawz.

Murder case

Due largely to a perceived lack of progress by law enforcement in the investigation of Shakur's murder, many independent investigations and theories emerged. Because of the acrimony between Shakur and Biggie (who was murdered in March 1997), there was speculation from the outset about the possibility of Biggie's involvement. Biggie, as well as his family, relatives, and associates, vehemently denied all such accusations. In 2002, the ''LA Times'' published a story by Pulitzer Prize-winning investigative reporter Chuck Philips, who claimed to have uncovered evidence implicating Biggie, in addition to Anderson and the Southside Crips, in the attack. Philips quoted unnamed gang-member sources who claimed Biggie had ties to the Crips, often hiring them for security during West Coast appearances, and that Biggie colluded with the Crips to murder Shakur. In 2008, after The Smoking Gun reported that the documents relied upon by Philips for his story were fraudulent, the ''LA Times'' printed an official front-page retraction of Philips' story. Less than five months later, Philips accepted a buyout and left the ''LA Times''.

In support of their claims, Biggie's family submitted documentation to MTV suggesting that he was working in a New York recording studio the night of the drive-by shooting. His manager Wayne Barrow and fellow rapper James "Lil' Cease" Lloyd made public announcements denying Biggie's partaking in the crime and claimed further that they were both with him in the recording studio during the night of the event.

The high profile nature of the killing and ensuing gang violence caught the attention of English filmmaker Nick Broomfield, who made the documentary film ''Biggie & Tupac'' which examines the lack of progress in the case by speaking to those close to the two slain rappers and the investigation. Shakur's close childhood friend and member of Outlawz, Yafeu "Yaki Kadafi" Fula, was in the convoy when the drive-by occurred and indicated to police that he might be able to identify the assailants, however, he was shot and killed shortly thereafter in a housing project in Irvington.

A DVD titled ''Tupac: Assassination'' was released on October 23, 2007, more than eleven years after Shakur's murder. It explores aspects surrounding the event and provides fresh insights into the cold case with new details about the environment.

Legacy

At a Mobb Deep concert following the death of the famed icon and release of ''The Don Killuminati: The 7 Day Theory'', Cormega recalled in an interview that the fans were all shouting "Makaveli," and emphasized the influence of ''The Don Killuminati: The 7 Day Theory'' and of Shakur himself even in New York at the height of the media-dubbed 'intercoastal rivalry'. Tupac Shakur was also one of the few rappers that were paid a tribute during the Up in Smoke Tour that featured many west coast hip-hop artists.

Shakur is held in high esteem by other MCs – in the book ''How to Rap'', Bishop Lamont notes that Shakur “mastered every element, every aspect” of rapping and Fredro Starr of Onyx says Shakur, "was a master of the flow." "Every rapper who grew up in the Nineties owes something to Tupac," wrote 50 Cent. "He didn't sound like anyone who came before him." About.com for their part named Shakur the most influential rapper ever.

To preserve Shakur's legacy, his mother founded the Shakur Family Foundation (later re-named the Tupac Amaru Shakur Foundation or TASF) in 1997. The TASF's stated mission is to "provide training and support for students who aspire to enhance their creative talents." The TASF sponsors essay contests, charity events, a performing arts day camp for teenagers and undergraduate scholarships. The Foundation officially opened the Tupac Amaru Shakur Center for the Arts (TASCA) in Stone Mountain, Georgia, on June 11, 2005. On November 14, 2003, a documentary about Shakur entitled ''Tupac: Resurrection'' was released under the supervision of his mother and narrated entirely in his voice. It was nominated for Best Documentary in the 2005 Academy Awards. Proceeds will go to a charity set up by Shakur's mother Afeni. On April 17, 2003, Harvard University co-sponsored an academic symposium entitled "All Eyez on Me: Tupac Shakur and the Search for the Modern Folk Hero." The speakers discussed a wide range of topics dealing with Shakur's impact on everything from entertainment to sociology.

Many of the speakers discussed Shakur's status and public persona, including State University of New York at Buffalo English professor Mark Anthony Neal who gave the talk "Thug Nigga Intellectual: Tupac as Celebrity Gramscian" in which he argued that Shakur was an example of the "organic intellectual" expressing the concerns of a larger group. Professor Neal has also indicated in his writings that the death of Shakur has left a "leadership void amongst hip-hop artists." Neal further describes him as a "walking contradiction", a status that allowed him to "make being an intellectual accessible to ordinary people."

Professor of Communications Murray Forman, of Northeastern University, spoke of the mythical status about Shakur's life and death. He addressed the symbolism and mythology surrounding Shakur's death in his talk entitled "Tupac Shakur: O.G. (Ostensibly Gone)". Among his findings were that Shakur's fans have "succeeded in resurrecting Tupac as an ethereal life force." In "From Thug Life to Legend: Realization of a Black Folk Hero", Professor of Music at Northeastern University, Emmett Price, compared Shakur's public image to that of the trickster-figures of African-American folklore which gave rise to the urban "bad-man" persona of the post-slavery period. He ultimately described Shakur as a "prolific artist" who was "driven by a terrible sense of urgency" in a quest to "unify mind, body, and spirit".

Michael Eric Dyson, University of Pennsylvania Avalon Professor of Humanities and African American Studies and author of the book ''Holler If You Hear Me: Searching for Tupac Shakur'' indicated that Shakur "spoke with brilliance and insight as someone who bears witness to the pain of those who would never have his platform. He told the truth, even as he struggled with the fragments of his identity." At one Harvard Conference the theme was Shakur's impact on entertainment, race relations, politics and the "hero/martyr". In late 1997, the University of California, Berkeley offered a student-led course entitled "History 98: Poetry and History of Tupac Shakur."

In late 2003, the Makaveli Branded Clothing line was launched by Afeni. In 2005, Death Row released ''Tupac: Live at the House of Blues''. The DVD was the final recorded performance of Shakur's career, which took place on July 4, 1996, and features a plethora of Death Row artists. In August 2006, ''Tupac Shakur Legacy'' was released. The interactive biography was written by Jamal Joseph. It features unseen family photographs, intimate stories, and over 20 removable reproductions of his handwritten song lyrics, contracts, scripts, poetry, and other personal papers. Shakur's sixth posthumous studio album, ''Pac's Life'', was released on November 21, 2006. It commemorates the 10th anniversary of Shakur's death. He is still considered one of the most popular artists in the music industry .

According to ''Forbes'', in 2008 Shakur's estate made $15 million. In 2002, they recognized him as a Top Earning Dead celebrity coming in on number ten on their list.

Library of Congress

Shakur's hit song "Dear Mama" is one of 25 songs that was added to the National Recording Registry in 2010. The Library of Congress has called "Dear Mama" "a moving and eloquent homage to both the murdered rapper's own mother and all mothers struggling to maintain a family in the face of addiction, poverty and societal indifference." This honor comes seven days after his birthday, where the rapper would have been 39. Shakur is the third rapper to enter the library, behind Grandmaster Flash and Public Enemy.

Honors

In a 2005 Rolling Stones Magazine Vote, Tupac was named No.6 of the '100 immortal artists of all time' behind the likes of Elvis and Lennon.

MTV ranked him at No.2 on their list of ''The Greatest MCs of All Time''. Shakur was inducted into the Hip-Hop Hall of Fame in 2002.

Ranked No.3 on VH1's 50 Greatest Hip Hop Artists.

In 2003, MTV's "22 Greatest MCs" countdown listed Shakur as the "Number 1 MC", as voted by the viewers. In 2004, at the VH1 Hip Hop Honors Shakur was honored along with DJ Hollywood, Kool DJ Herc, KRS-One, Public Enemy, Run-D.M.C., Rock Steady Crew, and Sugarhill Gang. A ''Vibe'' magazine poll in 2004 rated Shakur "the greatest rapper of all time" as voted by fans. At the First Annual Turks & Caicos International Film Festival held on Tuesday, October 17, 2006, Shakur was honored for his undeniable voice and talent and as a performer who crossed racial, ethnic, cultural and medium lines; his mother accepted the award on his behalf. In 2008, The National Association Of Recording Merchandisers in conjunction with the Rock and Roll Hall of Fame recognized him as a very influential artist and has added him in their Definitive 200 list. On Wednesday, June 23, 2010, Shakur was inducted to the Library of Congress’s National Recording Registry. The seat of the Catholic Church released a list of 12 songs onto the social networking Web site's streaming music service. Among the artists included are Mozart, Muse and Dame Shirley Bassey; the list also includes Shakur's song "Changes", which was released two years after his shooting death on a greatest hits album in 1998. His double album, ''All Eyez on Me'', is one of the highest-selling rap albums of all time, with over 5 million copies of the album sold in the United States alone by April 1996; it was eventually certified 9x platinum in June 1998 by the RIAA.

Discography

Studio albums

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Film

Acting career

In addition to rapping and hip hop music, Shakur acted in films. He made his first film appearance in the motion picture ''Nothing But Trouble'', as part of a cameo by the Digital Underground. His first starring role was in the film ''Juice''. In this story, he played the character Bishop, a trigger happy teen, for which he was hailed by ''Rolling Stone'''s Peter Travers as "the film's most magnetic figure." He went on to star with Janet Jackson in ''Poetic Justice'' (for which he was nominated outstanding actor in 1994, but did not win) and with Duane Martin in ''Above the Rim''. After his death, three of Shakur's completed films, ''Bullet'', ''Gridlock'd'' and ''Gang Related'', were released.

He had also been slated to star in the Hughes brothers' film ''Menace II Society'' but was replaced by Larenz Tate after assaulting Allen Hughes as a result of a quarrel. Director John Singleton mentioned that he wrote the script for ''Baby Boy'' with Shakur in mind for the leading role. It was eventually filmed with Tyrese Gibson in his place and released in 2001, five years after Shakur's death. The film features a mural of Shakur in the protagonist's bedroom as well as featuring the song "Hail Mary" in the film's score.

Filmography

1991 ''Juice (film) ''Drexell's Class'' ''A Different World (TV series) ''Poetic Justice (1993 film) ''In Living Color'' ''Above the Rim'' ''Murder Was the Case: The Movie'' ''Bullet (1996 film) ''Gridlock'd'' ''Gang Related (film) ''Tupac: Resurrection'' ''Notorious (2009 film) Tupac ''Live 2 Tell''

Year !! Title !! Role !! Notes
	|	Nothing But Trouble (1991 film)>Nothing But Trouble''	Himself	(Brief appearance)
	1992	Juice'' ||	Bishop	First starring role
	1992	|	Himself	Season 1: "Cruisin'"
	1993	A Different World'' ||	Piccolo	Season 6: "Homie, Don't You Know Me?"
	1993	Poetic Justice'' ||	Lucky	Co-starred with Janet Jackson
	1993	|	Himself	Season 5: "Ike Turner and Hooch"
	1994	|	Birdie	Co-starred with Duane Martin
	1995	|	Himself	(Uncredited)
	1996	Bullet'' ||	Tank	Released one month after Shakur's death
	1997	|	Ezekiel 'Spoon' Whitmore	Released several months after Shakur's death
	1997	Gang Related'' ||	Detective Rodríguez	Shakur's last performance in a film
	2003	|	Himself	Official documentary film
	2009	Notorious'' ||	Himself (archive footage)	Portrayed by Anthony Mackie
	2011/2012	|	Himself (archive footage)	The official biographical motion picture of Tupac Shakur. The film is currently being filmed.
	20??	|	Screenwriter	(Written in 1995)

Documentaries

Shakur's life has been recognized in big and small documentaries each trying capture the many different events during his short lifetime, most notably the Academy Award–nominated ''Tupac: Resurrection'', released in 2003.

1997: ''Tupac Shakur: Thug Immortal''

1997: ''Tupac Shakur: Words Never Die'' (TV)

2001: ''Tupac Shakur: Before I Wake...''

2001: ''Welcome to Deathrow''

2002: ''Tupac Shakur: Thug Angel''

2002: ''Biggie & Tupac''

2002: ''Tha Westside''

2003: ''2Pac 4 Ever''

2003: ''Tupac: Resurrection''

2004: ''Tupac vs.''

2004: ''Tupac: The Hip Hop Genius'' (TV)

2006: ''So Many Years, So Many Tears''

2007: ''Tupac: Assassination''

2009: ''Tupac: Assassination II: Reckoning''

See also

List of best-selling music artists

List of number-one albums (United States)

List of number-one hits (United States)

References

Sources

. .

External links

2Pac Legacy (Official website)

Tupac Amaru Shakur Foundation for the Arts

Tupac Legacy Tour

Yaki Kadafi Official Website

Online catalog of Shakur's personal library from his apartment at the time of his death, online at LibraryThing

FBI file on Tupac Shakur

Category:1971 births Category:1996 deaths Category:African American film actors Category:African American poets Category:African American rappers Category:African American record producers Category:American hip hop record producers Category:American people convicted of assault Category:American screenwriters Category:American sex offenders Category:American shooting survivors Category:Atlantic Records artists Category:Death Row Records artists Category:Deaths by firearm in Nevada Category:Deaths from respiratory failure Category:English-language poets Category:Interscope Records artists Category:Murdered African-American people Category:Murdered entertainers Category:Murdered rappers Category:People from Baltimore, Maryland Category:People from Harlem Category:People from Marin County, California Category:People murdered in Nevada Category:Rappers from the San Francisco Bay Area Category:Road crew Category:Shakur family Category:Unsolved murders in the United States Category:West Coast hip hop musicians

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