# 37 (number)

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | thirty-seven | |||

Ordinal | 37th (thirty-seventh) | |||

Factorization | prime | |||

Prime | 12th | |||

Divisors | 1, 37 | |||

Greek numeral | ΛΖ´ | |||

Roman numeral | XXXVII | |||

Binary | 100101_{2} | |||

Ternary | 1101_{3} | |||

Quaternary | 211_{4} | |||

Quinary | 122_{5} | |||

Senary | 101_{6} | |||

Octal | 45_{8} | |||

Duodecimal | 31_{12} | |||

Hexadecimal | 25_{16} | |||

Vigesimal | 1H_{20} | |||

Base 36 | 11_{36} |

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

## In mathematics

- 37 is the 12th prime number, a permutable prime with 73 (which is the 21st prime number). 37 is the fifth lucky prime,
^{[1]}the first irregular prime,^{[2]}the third unique prime^{[3]}and the third cuban prime of the form^{[4]}

- [math]\displaystyle{ p = \frac{x^3 - y^3}{x - y} \qquad \left(x = y + 1\right). }[/math]

- 37 is the smallest prime that is not also a supersingular prime.
- 37 is a centered hexagonal number
^{[5]}and a star number.^{[6]} - Every positive integer is the sum of at most 37 fifth powers (see Waring's problem).
^{[7]} - 37 appears in the Padovan sequence, preceded by the terms 16, 21, and 28 (it is the sum of the first two of these).
^{[8]} - Since the greatest prime factor of 37
^{2}+ 1 = 1370 is 137, which is substantially more than 37 twice, 37 is a Størmer number.^{[9]} - 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.
^{[10]} - 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.
- 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.
- The sum of the squares of the first 37 primes is divisible by 37.
^{[11]}

## In science

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

### Astronomy

- Messier object M37, a magnitude 6.0 open cluster in the constellation Auriga
- The New General Catalogue object NGC 37, a spiral galaxy in the constellation Phoenix
- Kepler-37b is the smallest known planet.
- NGC 2169 is known as the 37 Cluster, due to its resemblance of the numerals.

## 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

**Thirty-seven** is:

- The number of the French department Indre-et-Loire
^{[12]} - 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 number of Great Nats traditionally worshiped in Burma
- The RSA public exponent used by PuTTY
- +37 was the international dialing code of the German Democratic Republic (aka East Germany). Today the +37 prefix is shared by Lithuania (+370), Latvia (+371), Estonia (+372), Moldova (+373), Armenia (+374),
*Belarus*(+375), Andorra (+376), Monaco (+377), San Marino (+378) and Vatican City (+379). - The number of seconds of church-bell and thunderstorm recording before the opening tritone riff in the song "Black Sabbath" on the album
*Black Sabbath*by the band Black Sabbath, which is considered to mark the birth of heavy metal music. - 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)

## References

- ↑ "Sloane's A031157: Numbers that are both lucky and prime". OEIS Foundation. https://oeis.org/A031157.
- ↑ "Sloane's A000928: Irregular primes". OEIS Foundation. https://oeis.org/A000928.
- ↑ "Sloane's A040017: Unique period primes". OEIS Foundation. https://oeis.org/A040017.
- ↑ "Sloane's A002407: Cuban primes". OEIS Foundation. https://oeis.org/A002407.
- ↑ "Sloane's A003215: Hex (or centered hexagonal) numbers". OEIS Foundation. https://oeis.org/A003215.
- ↑ "Sloane's A003154: Centered 12-gonal numbers. Also star numbers". OEIS Foundation. https://oeis.org/A003154.
- ↑ Weisstein, Eric W.. "Waring's Problem" (in en). https://mathworld.wolfram.com/WaringsProblem.html.
- ↑ "Sloane's A000931: Padovan sequence". OEIS Foundation. https://oeis.org/A000931.
- ↑ "Sloane's A005528: Størmer numbers". OEIS Foundation. https://oeis.org/A005528.
- ↑ Vukosav, Milica (2012-03-13). "NEKA SVOJSTVA BROJA 37" (in hr).
*Matka: Časopis za Mlade Matematičare***20**(79): 164. ISSN 1330-1047. https://hrcak.srce.hr/81042. - ↑ 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)". OEIS Foundation. https://oeis.org/A111441. Retrieved 2022-06-02.
- ↑ "INDRE-ET-LOIRE: map, cities and data of the departement of Indre-et-Loire 37". http://www.map-france.com/department-Indre-et-Loire/.

## External links

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

Original source: https://en.wikipedia.org/wiki/37 (number).
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