Answer to Question #161087 in Combinatorics | Number Theory for Geek

Question

Determine if n=161304001 is a strong pseudo prime with respect to the base 2.

Answer 1

Let $n=161304001$

$n-1=161304000=2^6\cdot2520375\\ 2^{2520375}\equiv 30275048 \not\equiv 1 \text{ mod }161304001\\ 2^{2 \cdot 2520375}\equiv -1 \text { mod } 161304001$

This shows that n is composite and also passes the Miller-Rabi test. Hence, n=161304001 is a strong pseudoprime.