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.