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Sigma(56) equals the first prime of the form 6n  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 doubledigit 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]
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