Primality proof for n = 145295143558111:

Take b = 3.

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

2534364967 is prime.
b^((n-1)/2534364967)-1 mod n = 69216082370408, which is a unit, inverse 75121499342418.

(2534364967) divides n-1.

(2534364967)^2 > n.

n is prime by Pocklington's theorem.