# 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]

2^{5} is the highest known power with all decimal digits being prime. [Kulsha]

M_{32} 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.

2^{32} - 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 + 29.

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 (^{3}2=16), while the index of that prime comes by turning the second
digit (1st prime) into an exponent (3^{2}=9, with 23=p_{9}). [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]