# 37

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Cardinalthirty-seven
Ordinal37th
(thirty-seventh)
Factorizationprime
Prime12th
Divisors1, 37
Greek numeralΛΖ´
Roman numeralXXXVII
Binary1001012
Ternary11013
Senary1016
Octal458
Duodecimal3112

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 phàn nàn 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:

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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 kết thúc 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 toàn thân temperature in degrees Celsius

### Astronomy

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

## In other fields

Thirty-seven is:

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• The number of the French department Indre-et-Loire
• The number of slots in European roulette (numbered 0 to lớn 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.