# 57

This number is a composite.

π(57) = 24 and 5757 - 24 is prime. [Noll]

57 * 225 - 1 is prime. [Noll]

57 + (100 * 2n) 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 * 21828 + 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 Fools prime that is the sum of first n April Fools primes, i.e., (9 + 21 + 27), (case n=3). [Loungrides]

The smallest double-digit odd number that creates two primes (5657 and 5857) by concatenation with its previous and next even numbers. [Loungrides]

Is 57 a prime number? The online computer game “Is this prime?” tests a player’s knowledge of prime numbers. Give it a whirl.

(There is one curio for this number that has not yet been approved by an editor.)