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 is the only two digit number in base 10 whose product, when multiplied by two, subtracted by one, and then read backwards, equals the original two digit number: 37×2=74, 74-1=73, 73 backwards is 37.
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.