Primality proof for n = 1435773091665945871:

Take b = 2.

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

1553407 is prime.
b^((n-1)/1553407)-1 mod n = 79438728289737084, which is a unit, inverse 607403481233932245.

879331 is prime.
b^((n-1)/879331)-1 mod n = 382739370402427132, which is a unit, inverse 671375227969058660.

(879331 * 1553407) divides n-1.

(879331 * 1553407)^2 > n.

n is prime by Pocklington's theorem.