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.