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.