This number is a prime.
7^1172 - 1172^11; a prime of form 7^n - n^11, similar to Pomerance's Convenience Store numbers (see entry for PC 1999). It was certified prime with Primo. Also, if we sum the factorials of the digits of 7^1172 - 1172^11 we get 38125657, a prime. [Earls]