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.