Primality proof for n = 156765911253115553:

Take b = 2.

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

923685781 is prime.
b^((n-1)/923685781)-1 mod n = 24793373552360192, which is a unit, inverse 26445239365314554.

(923685781) divides n-1.

(923685781)^2 > n.

n is prime by Pocklington's theorem.