Primality proof for n = 752881:

Take b = 2.

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

3137 is prime.
b^((n-1)/3137)-1 mod n = 734443, which is a unit, inverse 156840.

(3137) divides n-1.

(3137)^2 > n.

n is prime by Pocklington's theorem.