# 32

This number is a composite. 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] 32 +/- 3^2 are both prime. [Homewood] The smallest number n such that all the positive values of n-3^k are all primes, (i.e., k=0, 1, 2, 3). [Loungrides] Half of this reversal of a prime may be had by turning its first digit (2nd prime) into a tetration superscript (32=16), while the index of that prime comes by turning the second digit (1st prime) into an exponent (32=9, with 23=p9). [Merickel] The smallest Honaker number is also a Happy number. [Gupta] π(32) is the (3+2)th prime. The smallest prime-digit number of this form. [Bajpai] The number of primes consisting of all distinct odd digits only. Note that a dozen of them (six pairs) are emirps. [Loungrides] 32-3^2 is prime. [Silva] The smallest Honaker number equals two to the power (3+2). [Ramsey] The "minimal prime problem" in base-32 cannot be proven. [Xayah]