Primality proof for n = 65099:

Take b = 2.

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

269 is prime.
b^((n-1)/269)-1 mod n = 52923, which is a unit, inverse 34918.

(269) divides n-1.

(269)^2 > n.

n is prime by Pocklington's theorem.