Primality proof for n = 2151858718037429125511251:

Take b = 2.

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

20387630040577 is prime.
b^((n-1)/20387630040577)-1 mod n = 1609459712269279077779375, which is a unit, inverse 72744713369542696959983.

(20387630040577) divides n-1.

(20387630040577)^2 > n.

n is prime by Pocklington's theorem.