37 (number)

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

Cardinal 37
thirty-seven
Ordinal 37th
thirty-seventh
Factorization prime
Divisors 1, 37
Roman numeral XXXVII
Binary 0100101
Hexadecimal 25

Contents

[edit] In mathematics

It is a prime number, 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).

It is a factor of all 3-digit base 10 repdigits, such as 111. 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.

[edit] In science

[edit] Astronomy

[edit] In other fields

House number in Baarle (Belgian part)
House number in Baarle (Belgian part)

Thirty-seven is:

[edit] Historical years

37 B.C., 37 A.D., 1937, 2037

[edit] Related links