2521

This number is a prime.

(2 * 2521) - 1 = 71² and 2 * (2521 - 1) = 7!. [Forslund]

2521 minus one is the smallest EPRN.

2521² = 1456³ - 1455³, i.e., one solution to the Diophantine equation z² = x³ - y³. A Diophantine equation is a polynomial equation in which only integer solutions are allowed. These are named after the Greek algebraist Diophantus who lived in the 3rd century. [Mizuki]

The smallest prime formed by concatenating consecutive composite odd numbers. [Green]

The smallest prime that can be represented as the product of a number n and its reversal plus 1, in two ways, (n=120 and n=210). [Loungrides]

The smallest prime p such that p ≡ 1 mod d , where d stands for any of the digits 2 through 9. [Beedassy]