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.