Primality proof for n = 1674656872585139:

Take b = 2.

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

41802583 is prime.
b^((n-1)/41802583)-1 mod n = 1429771371734283, which is a unit, inverse 902297332204876.

(41802583) divides n-1.

(41802583)^2 > n.

n is prime by Pocklington's theorem.