Primality proof for n = 761069:
Take b = 2.
b^(n-1) mod n = 1.
353 is prime.
b^((n-1)/353)-1 mod n = 344337, which is a unit, inverse 558310.
11 is prime.
b^((n-1)/11)-1 mod n = 659772, which is a unit, inverse 498113.
(11 * 353) divides n-1.
(11 * 353)^2 > n.
n is prime by Pocklington's theorem.