Primality proof for n = 63589:

Take b = 2.

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

757 is prime.
b^((n-1)/757)-1 mod n = 39868, which is a unit, inverse 39401.

(757) divides n-1.

(757)^2 > n.

n is prime by Pocklington's theorem.