Primality proof for n = 1151:
Take b = 2.
b^(n-1) mod n = 1.
23 is prime.
b^((n-1)/23)-1 mod n = 199, which is a unit, inverse 937.
5 is prime.
b^((n-1)/5)-1 mod n = 1059, which is a unit, inverse 588.
(5^2 * 23) divides n-1.
(5^2 * 23)^2 > n.
n is prime by Pocklington's theorem.