Primality proof for n = 46076956964474543:

Take b = 2.

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

704251 is prime.
b^((n-1)/704251)-1 mod n = 14924512230972256, which is a unit, inverse 14499061334772664.

78283 is prime.
b^((n-1)/78283)-1 mod n = 26474877516403236, which is a unit, inverse 41560644167870315.

(78283 * 704251) divides n-1.

(78283 * 704251)^2 > n.

n is prime by Pocklington's theorem.