4091

This number is a prime.

The 563rd prime and 5 + 6 + 3 = 4 + 0 + 9 + 1. Note that it is the first prime with this property containing all distinct digits. [Bopardikar]

The smallest prime of form n^((n+1)*(n+2))-(n+3), where n > 1. [Vago]

The smallest Honaker prime that is an anagram of a smaller Honaker prime (1049). [Gaydos]