# 37 (number)

 ← 36 37 38 →
Cardinal thirty-seven
Ordinal 37th
(thirty-seventh)
Factorization prime
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, the first irregular prime, the third unique prime and the third cuban prime of the form

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

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

It is a centered hexagonal number and a star number.

37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.

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 obviously more than 37 twice, 37 is a Størmer number.

37 has the property that when its digits are reversed, the resulting number is one less than a multiple of the original number. The only other two digit number in base 10 with this property is 14.

37 is the only two digit number in base 10 with the following property: The difference between the two digits equals the square root of the difference between the number itself and the least common multiple of the two digits.

## 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: