1289

This number is a prime.

This Sophie Germain prime is also a twin prime, and the smallest prime having distinct or increasing digits and exactly 5 permutations of its digits prime. [Hasler]

Concatenate (left-to-right) the 1st, 2nd, 8th, and 9th prime and you will get another prime, i.e., 231923. [Loungrides]

Smallest four-digit prime number for which the product of each digit is the square of the first two digits. [Deshpande]

On an infinite spiral-numbered chessboard, if a queen starts from 1 (centre of the spiral) and repeatedly moves to the nearest unvisited prime-numbered square, then eventually the queen can no longer move after, at square number 1289. [Gudipati]