Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.

The property of being prime (or not) is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and . Algorithms much more efficient than trial division have been devised to test the primality of large numbers. These include the Miller–Rabin primality test, which is fast but has a small probability of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits.

Subprime lending

In finance, subprime lending (also referred to as near-prime, non-prime, and second-chance lending) means making loans to people who may have difficulty maintaining the repayment schedule, sometimes reflecting setbacks, such as unemployment, divorce, medical emergencies, etc. Historically, subprime borrowers were defined as having FICO scores below 640, although "this has varied over time and circumstances."

These loans are characterized by higher interest rates, poor quality collateral, and less favorable terms in order to compensate for higher credit risk. Many subprime loans were packaged into mortgage-backed securities (MBS) and ultimately defaulted, contributing to the financial crisis of 2007–2008.

Proponents of subprime lending maintain that the practice extends credit to people who would otherwise not have access to the credit market. Professor Harvey S. Rosen of Princeton University explained, "The main thing that innovations in the mortgage market have done over the past 30 years is to let in the excluded: the young, the discriminated-against, the people without a lot of money in the bank to use for a down payment."

Prime (order theory)

In mathematics, an element p of a partial order (P, ≤) is a meet prime element when p is the principal element of a principal prime ideal. Equivalently, if P is a lattice, p ≠ top, and for all a, b in P,

See also

References

Blue

Blue is the colour between violet and green on the optical spectrum of visible light. Human eyes perceive blue when observing light with a wavelength between 450 and 495 nanometres. Blues with a higher frequency and thus a shorter wavelength gradually look more violet, while those with a lower frequency and a longer wavelength gradually appear more green. Pure blue, in the middle, has a wavelength of 470 nanometres. In painting and traditional colour theory, blue is one of the three primary colours of pigments, along with red and yellow, which can be mixed to form a wide gamut of colours. Red and blue mixed together form violet, blue and yellow together form green. Blue is also a primary colour in the RGB colour model, used to create all the colours on the screen of a television or computer monitor.

The modern English word blue comes from Middle English bleu or blewe, from the Old French bleu, a word of Germanic origin, related to the Old High German word blao. The clear sky and the deep sea appear blue because of an optical effect known as Rayleigh scattering. When sunlight passes through the atmosphere, the blue wavelengths are scattered more widely by the oxygen and nitrogen molecules, and more blue comes to our eyes. Rayleigh scattering also explains blue eyes; there is no blue pigment in blue eyes. Distant objects appear more blue because of another optical effect called atmospheric perspective.

Blue (Down by Law album)

Blue is the second full-length album by the punk rock band Down by Law.

Track listing

Personnel

Shades of blue

Varieties of the color blue may differ in hue, chroma (also called saturation, intensity, or colorfulness), or lightness (or value, tone, or brightness), or in two or three of these qualities. Variations in value are also called tints and shades, a tint being a blue or other hue mixed with white, a shade being mixed with black. A large selection of these various colors is shown below.

Tints of blue

In this section, the term tint is used in its technical sense as used in color theory, meaning a blueish color mixed with white or light gray.

Periwinkle

Shown in the right is the color periwinkle, or periwinkle blue. Another name for this color is lavender blue. The color is a mixture of white and blue. It is named after the Periwinkle flower and is also commonly referred to as a tone of light blue.

Powder blue

The web color powder blue is shown on the right.

The first recorded use of powder blue as a color name in English was in 1774.

Light blue

The web color light blue is displayed in the color box at right. Variations of this color are known as sky blue, baby blue, or angel blue. Within the X11 color system, with a hue code of 194, this color is closer to cyan than to blue.

Remix (book)

Remix: Making Art and Commerce Thrive in the Hybrid Economy is Lawrence Lessig's fifth book. It is available as a free download under a Creative Commons license. It details a hypothesis about the societal effect of the Internet, and how this will affect production and consumption of popular culture.

Summary

In Remix Lawrence Lessig, a Harvard law professor and a respected voice in what he deems the "copyright wars", describes the disjuncture between the availability and relative simplicity of remix technologies and copyright law. Lessig insists that copyright law as it stands now is antiquated for digital media since every "time you use a creative work in a digital context, the technology is making a copy" (98). Thus, amateur use and appropriation of digital technology is under unprecedented control that previously extended only to professional use.

Lessig insists that knowledge and manipulation of multi-media technologies is the current generation's form of "literacy"- what reading and writing was to the previous. It is the vernacular of today. The children growing up in a world where these technologies permeate their daily life are unable to comprehend why "remixing" is illegal. Lessig insists that amateur appropriation in the digital age cannot be stopped but only 'criminalized'. Thus most corrosive outcome of this tension is that generations of children are growing up doing what they know is "illegal" and that notion has societal implications that extend far beyond copyright wars. The book is now available as a free download under one of the Creative Commons' licenses.