Primality proof for n = 47907599:

Take b = 2.

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

34367 is prime.
b^((n-1)/34367)-1 mod n = 40099037, which is a unit, inverse 46304264.

(34367) divides n-1.

(34367)^2 > n.

n is prime by Pocklington's theorem.