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 Stormer number.

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