Primality proof for n = 762707485068427817:

Take b = 2.

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

95338435633553477 is prime.
b^((n-1)/95338435633553477)-1 mod n = 255, which is a unit, inverse 155532506759051947.

(95338435633553477) divides n-1.

(95338435633553477)^2 > n.

n is prime by Pocklington's theorem.