# 37 (number)

Short description: Natural number
 ← 36 37 38 →
Cardinalthirty-seven
Ordinal37th
(thirty-seventh)
Factorizationprime
Prime12th
Divisors1, 37
Greek numeralΛΖ´
Roman numeralXXXVII
Binary1001012
Ternary11013
Quaternary2114
Quinary1225
Senary1016
Octal458
Duodecimal3112
Vigesimal1H20
Base 361136

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

## In mathematics

$\displaystyle{ p = \frac{x^3 - y^3}{x - y} \qquad \left(x = y + 1\right). }$
• 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 372 + 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 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:

• 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 .

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

## References

1. "Sloane's A000928: Irregular primes". OEIS Foundation.
2. "Sloane's A040017: Unique period primes". OEIS Foundation.
3. "Sloane's A002407: Cuban primes". OEIS Foundation.
4. "Sloane's A003215: Hex (or centered hexagonal) numbers". OEIS Foundation.
5. Weisstein, Eric W.. "Waring's Problem" (in en).
6. "Sloane's A000931: Padovan sequence". OEIS Foundation.
7. "Sloane's A005528: Størmer numbers". OEIS Foundation.
8. Vukosav, Milica (2012-03-13). "NEKA SVOJSTVA BROJA 37" (in hr). Matka: Časopis za Mlade Matematičare 20 (79): 164. ISSN 1330-1047.
9. 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. Retrieved 2022-06-02.