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.