# 57

This number is a composite.

π(57) = 2^{4} and 57^{57} - 2^{4} is prime. [Noll]

57 * 2^{25} - 1 is prime. [Noll]

57 + (100 * 2^{n}) are primes for *n* = -1, 0, 1, 2, 3, 4, and 5. [Luhn]

Every number greater than 57 is (probably) the sum of distinct primes greater than eleven. [Capelle]

57 * 2^{1828} + 1 is a Proth prime as well as a
generalized Cullen prime. [Wesolowski]

57 + 5^(5+7) + 7^(5+7) is prime. [Silva]

Jokingly known as the "Grothendieck prime."

Prime numbers that end with "57" occur more often than any other two-digit ending among the first 1000 primes. [Honaker]

The smallest April Fool prime that is the sum of first *n*
April Fool primes, i.e., (9 + 21 + 27), (case n=3). [Loungrides]

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