7549

This number is a prime.

A prime equal to the concatenation of the four single-digit primes plus their sum: 7532 + (7+5+3+2). [Silva]

The largest known prime such that p - x² is composite for x = 1...sqrt(p). [Crespi de Valldaura]

Probably the largest prime not of the form p + k^2, with p prime and k > 0. [Russo]