Primality proof for n = 41802583:
Take b = 2.
b^(n-1) mod n = 1.
50123 is prime. b^((n-1)/50123)-1 mod n = 13658778, which is a unit, inverse 20082567.
(50123) divides n-1.
(50123)^2 > n.
n is prime by Pocklington's theorem.