← 36 37 38 →
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.

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 sports

José María López used this number during his successful years in the World Touring Car Championship from 2014 until 2016. He still uses this number in Formula E since joining in 2016-17 season with DS Virgin Racing.

## In other fields House number in Baarle (in its Belgian part)

Thirty-seven is:

1. ^ "Sloane's A040017: Unique period primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. ^ "Sloane's A000928: Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. ^ Sloane, N. J. A. (ed.). "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-05.
4. ^ "Sloane's A002407: Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. ^ "Sloane's A031157: Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. ^ "Sloane's A003154: Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
7. ^ "Sloane's A003215: Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
8. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
9. ^ Weisstein, Eric W. "Waring's Problem". mathworld.wolfram.com. Retrieved 2020-08-21.
10. ^ "Sloane's A000931: Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
11. ^ "Sloane's A005528: Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
12. ^ Vukosav, Milica (2012-03-13). "NEKA SVOJSTVA BROJA 37". Matka: Časopis za Mlade Matematičare (in Croatian). 20 (79): 164. ISSN 1330-1047.
13. ^