Primality proof for n = 70627:
Take b = 2.
b^(n-1) mod n = 1.
149 is prime.
b^((n-1)/149)-1 mod n = 67623, which is a unit, inverse 33174.
79 is prime.
b^((n-1)/79)-1 mod n = 11836, which is a unit, inverse 28505.
(79 * 149) divides n-1.
(79 * 149)^2 > n.
n is prime by Pocklington's theorem.