# 56

Sigma(56) equals the first prime of the form 6*n* - 1 factorial, 5!. [Noll]

2^{56 - 1} - 56 + 1 is prime. [Noll]

The number of products of distinct primes less than or equal to 11 (the only palindromic prime with an even number of digits) which are congruent to -1 mod 11 is 56. [Noll]

D. H. Lehmer showed that Meissel's calculation of primes less than a billion was 56 too few.

The product of all composite numbers up to 56 (i.e. Compositorial 56) plus 1 is prime. Note that this prime consist of 56 digits. [Gupta]

56 = sigma(sigma(sigma(5+6))). 56 is the smallest multidigit number with this property and there is only one other. [Firoozbakht]

The smallest number that can be expressed as a sum of two distinct primes, each ending with the digit 3, in two different ways (56 = 3 + 53 = 13 + 43). [Sladcik]

prime(56) = prime(5)*prime(6)+sigma(56). 56 is the only known number (up to 3*10^8) with this property. [Firoozbakht]

. (56, 58) is the only pair of successive double-digit even composite numbers m, n with composite reversals, R(m), R(n), such that m^4 + [R(m)]^4 and n^4 + [R(n)]^4, i.e., 56^4 + 65^4 and 58^4 + 85^4, are also primes. [Loungrides]