37 (number)

← 36 37 38 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-seven
Ordinal	37th (thirty-seventh)
Factorization	prime
Prime	12th
Divisors	1, 37
Greek numeral	ΛΖ´
Roman numeral	XXXVII
Binary	1001012
Ternary	11013
Senary	1016
Octal	458
Duodecimal	3112
Hexadecimal	2516

37 (thirty-seven) is the natural number following 36 and preceding 38.

In mathematics

37 is the 12th prime number and the third unique prime in decimal. 37 is the first irregular prime, and the third isolated prime without a twin prime. It is also the third cuban prime, the fourth emirp, and the fifth lucky prime.

• 37 is the third star number and the fourth centered hexagonal number.
• The sum of the squares of the first 37 primes is divisible by 37.
• Every positive integer is the sum of at most 37 fifth powers (see Waring's problem).
• 37 appears in the Padovan sequence, preceded by the terms 16, 21, and 28 (it is the sum of the first two of these).
• Since the greatest prime factor of 37² + 1 = 1370 is 137, which is substantially more than 37 twice, 37 is a Størmer number.

The smallest magic square, using only primes and 1, contains 37 as the value of its central cell:

31	73	7
13	37	61
67	1	43

Its magic constant is 37 x 3 = 111, where 3 and 37 are the first and third decimal unique primes (the second such prime is 11).

In base-ten, 37 is a permutable prime with 73, which is the 21st prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime.

In moonshine theory, whereas all p ⩾ 73 are non-supersingular primes, the smallest such prime is 37.

There are exactly 37 complex reflection groups.

In decimal

For a three-digit number that is divisible by 37, a rule of divisibility is that another divisible by 37 can be generated by transferring first digit onto the end of a number. For example: 37|148 ➜ 37|481 ➜ 37|814.

Any multiple of 37 can be mirrored and spaced with a zero each for another multiple of 37. For example, 37 and 703, 74 and 407, and 518 and 80105 are all multiples of 37.

Any multiple of 37 with a three-digit repunit inserted generates another multiple of 37. For example, 30007, 31117, 74, 70004 and 78884 are all multiples of 37.

In science

• The atomic number of rubidium
• The normal human body temperature in degrees Celsius

Astronomy

• NGC 2169 is known as the 37 Cluster, due to its resemblance of the numerals.

In other fields

House number in Baarle (in its Belgian part)

Thirty-seven is:

• The number of the French department Indre-et-Loire
• The number of slots in European roulette (numbered 0 to 36, the 00 is not used in European roulette as it is in American roulette)
• The RSA public exponent used by PuTTY
• Richard Nixon, 37th president of the United States.

See also

• List of highways numbered 37
• Number Thirty-Seven, Pennsylvania, unincorporated community in Cambria County, Pennsylvania
• I37 (disambiguation)

External links

• 37 Heaven Large collection of facts and links about this number.