Primality proof for n = 46879411:

Take b = 2.

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

1562647 is prime.
b^((n-1)/1562647)-1 mod n = 42394781, which is a unit, inverse 44942311.

(1562647) divides n-1.

(1562647)^2 > n.

n is prime by Pocklington's theorem.