Primality proof for n = 70825721:

Take b = 2.

b^(n-1) mod n = 1.

252949 is prime.
b^((n-1)/252949)-1 mod n = 10924806, which is a unit, inverse 36789724.

(252949) divides n-1.

(252949)^2 > n.

n is prime by Pocklington's theorem.