# 37 (number)

 ← 36 37 38 →
Cardinal thirty-seven
Ordinal 37th
(thirty-seventh)
Factorization prime
Prime 12th
Divisors 1, 37
Roman numeral XXXVII
Binary 1001012
Ternary 11013
Quaternary 2114
Quinary 1225
Senary 1016
Octal 458
Duodecimal 3112
Vigesimal 1H20
Base 36 1136

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

## In mathematics

Thirty-seven 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]

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

37 is the smallest prime that is not also a supersingular prime.

It 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).

37 appears in the Padovan sequence, preceded by the terms 16, 21, and 28 (it is the sum of the first two of these).[7]

Since the greatest prime factor of 372 + 1 = 1370 is 137, which is substantially more than 37 twice, 37 is a Størmer number.[8]

## In sports

The jersey number 37 has been retired by several North American sports teams in honor of past greats:

## In other fields

House number in Baarle (in its Belgian part)

Thirty-seven is:

## References

1. ^ "Sloane's A031157 : Numbers that are both lucky and prime". 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's A040017 : Unique period primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". 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 A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
8. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
9. ^ Spencer, Adam (2004). Adam Spencer's Book of Numbers. New York: Four Walls Eight Windows. p. 61.
10. ^ Random numbers