The smallest two-digit number such that phi(n) + sigma(n) is prime. [Russo]
32! - 1 and (32 + 1)! - 1 are primes. [Gallot]
25 is the highest known power with all decimal digits being prime. [Kulsha]
M32 contains all known prime factors of form 2^2^k+1 in logical order, where k = 0 to 4. [Luhn]
It is not known if there exists a
mean gap of exactly 32 between the first n successive
primes.
232 - 1 is the product of the first Fermat primes which are known (3, 5, 17, 257, 65537). [Capelle]
The only even number formed from two consecutive
primes. [Silva]
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