Primality proof for n = 245035279530995029:

Take b = 2.

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

402021673 is prime.
b^((n-1)/402021673)-1 mod n = 233229203073433635, which is a unit, inverse 27546935882754072.

6553 is prime.
b^((n-1)/6553)-1 mod n = 191678323037400532, which is a unit, inverse 199424989229701615.

(6553 * 402021673) divides n-1.

(6553 * 402021673)^2 > n.

n is prime by Pocklington's theorem.