Primality proof for n = 375799:
Take b = 2.
b^(n-1) mod n = 1.
62633 is prime. b^((n-1)/62633)-1 mod n = 63, which is a unit, inverse 280358.
(62633) divides n-1.
(62633)^2 > n.
n is prime by Pocklington's theorem.