4111

This number is a prime.

The number of digits in the sixth (and largest known) palindromic prime formed from the reflected decimal expansion of π. It was found by Eric Weisstein in May 2006.

The smallest prime p whose smallest positive primitive root (mod p) is not squarefree. [Vantieghem]

Euler's number has a nice rational approximation: e ≈ 11175/4111 (two digits out of three are '1's). Note the denominator is a near-repunit prime. [Leonardis]