Primality proof for n = 145091:

Take b = 2.

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

1319 is prime.
b^((n-1)/1319)-1 mod n = 27960, which is a unit, inverse 6170.

(1319) divides n-1.

(1319)^2 > n.

n is prime by Pocklington's theorem.