Primality proof for n = 25121:
Take b = 2.
b^(n-1) mod n = 1.
157 is prime.
b^((n-1)/157)-1 mod n = 2098, which is a unit, inverse 21924.
5 is prime.
b^((n-1)/5)-1 mod n = 15065, which is a unit, inverse 17849.
(5 * 157) divides n-1.
(5 * 157)^2 > n.
n is prime by Pocklington's theorem.