Primality proof for n = 137849:
Take b = 2.
b^(n-1) mod n = 1.
17231 is prime. b^((n-1)/17231)-1 mod n = 255, which is a unit, inverse 89737.
(17231) divides n-1.
(17231)^2 > n.
n is prime by Pocklington's theorem.