3251

This number is a prime.

The larger term in the only pair of 4-digit emirps, (1523, 3251), whose both terms are of form x^2+2x+3, x > 0, (x=38 and x=56). [Loungrides]

The prime number 3251 multiplied by one of the numbers 86, 172, 344 or 688, gives the concatenation of a multiple of 559 with 86, 172, 344 or 688. [Galliani]

Smallest odd prime p such that (174^p-1)/173 is (probable) prime. [Luen]

The smallest prime in the first set of eight consecutive primes {3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307} whose sum of digits is prime. [Bajpai]

3251 is the smallest prime congruent to 456 (mod 559). [Galliani]