Primality proof for n = 76471:
Take b = 2.
b^(n-1) mod n = 1.
2549 is prime. b^((n-1)/2549)-1 mod n = 12512, which is a unit, inverse 23231.
(2549) divides n-1.
(2549)^2 > n.
n is prime by Pocklington's theorem.