Primality proof for n = 875803:

Take b = 2.

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

145967 is prime.
b^((n-1)/145967)-1 mod n = 63, which is a unit, inverse 152918.

(145967) divides n-1.

(145967)^2 > n.

n is prime by Pocklington's theorem.