Primality proof for n = 1940901878027589158559608212721:

Take b = 2.

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

426050702417 is prime.
b^((n-1)/426050702417)-1 mod n = 623925913228564101241520854055, which is a unit, inverse 1821014813758900622500848532134.

93179 is prime.
b^((n-1)/93179)-1 mod n = 164260977705796339867697392344, which is a unit, inverse 1580256537309896012768527145117.

(93179 * 426050702417) divides n-1.

(93179 * 426050702417)^2 > n.

n is prime by Pocklington's theorem.