Primality proof for n = 765448337:
Take b = 2.
b^(n-1) mod n = 1.
47840521 is prime. b^((n-1)/47840521)-1 mod n = 65535, which is a unit, inverse 130605681.
(47840521) divides n-1.
(47840521)^2 > n.
n is prime by Pocklington's theorem.