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.