Primality proof for n = 1635296843:
Take b = 2.
b^(n-1) mod n = 1.
29581 is prime.
b^((n-1)/29581)-1 mod n = 1348274699, which is a unit, inverse 554847727.
211 is prime.
b^((n-1)/211)-1 mod n = 351363295, which is a unit, inverse 674649744.
(211 * 29581) divides n-1.
(211 * 29581)^2 > n.
n is prime by Pocklington's theorem.