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.