Primality proof for n = 1249292843947:

Take b = 2.

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

3670871 is prime.
b^((n-1)/3670871)-1 mod n = 1130826922106, which is a unit, inverse 151661628123.

(3670871) divides n-1.

(3670871)^2 > n.

n is prime by Pocklington's theorem.