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.