Primality proof for n = 292386187:
Take b = 2.
b^(n-1) mod n = 1.
5879 is prime.
b^((n-1)/5879)-1 mod n = 130453607, which is a unit, inverse 4206811.
307 is prime.
b^((n-1)/307)-1 mod n = 114336306, which is a unit, inverse 283400995.
(307 * 5879) divides n-1.
(307 * 5879)^2 > n.
n is prime by Pocklington's theorem.