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.