Primality proof for n = 701527:
Take b = 2.
b^(n-1) mod n = 1.
16703 is prime. b^((n-1)/16703)-1 mod n = 470934, which is a unit, inverse 569325.
(16703) divides n-1.
(16703)^2 > n.
n is prime by Pocklington's theorem.