Primality proof for n = 21561596637519154364530566979:

Take b = 2.

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

156765911253115553 is prime.
b^((n-1)/156765911253115553)-1 mod n = 9002307714681038498645114615, which is a unit, inverse 8012647576243137840621811138.

(156765911253115553) divides n-1.

(156765911253115553)^2 > n.

n is prime by Pocklington's theorem.