Primality proof for n = 2376645121788851:

Take b = 2.

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

26510263489 is prime.
b^((n-1)/26510263489)-1 mod n = 464543367787578, which is a unit, inverse 282098339281732.

(26510263489) divides n-1.

(26510263489)^2 > n.

n is prime by Pocklington's theorem.