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.