Primality proof for n = 149899:
Take b = 2.
b^(n-1) mod n = 1.
83 is prime.
b^((n-1)/83)-1 mod n = 42108, which is a unit, inverse 66744.
43 is prime.
b^((n-1)/43)-1 mod n = 7457, which is a unit, inverse 84528.
(43 * 83) divides n-1.
(43 * 83)^2 > n.
n is prime by Pocklington's theorem.