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]
It is not known if there exists a mean gap of exactly 32 between the first n successive primes.
The only even number formed from two consecutive primes. [Silva]
The smallest Honaker number.
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]
(32) is the (3+2)th prime. The smallest prime-digit number of this form. [Bajpai]
32-3^2 is prime. [Silva]
(There are 4 curios for this number that have not yet been approved by an editor.)