Primality proof for n = 39295853:

Take b = 2.

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

118361 is prime.
b^((n-1)/118361)-1 mod n = 19339856, which is a unit, inverse 27491427.

(118361) divides n-1.

(118361)^2 > n.

n is prime by Pocklington's theorem.