15359

This number is a prime.

Let p(i) be the ith prime. Then p(k)# < _k²C_k = (k²)!/(k!*(k²-k)!) for 2 < k < 1794. But p(k)# > (k²)!/(k!*(k²-k)!) for k ≥ 1794. What is this key prime p(k)? 15359. [Caldwell]