Primality proof for n = 75707:

Take b = 2.

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

37853 is prime.
b^((n-1)/37853)-1 mod n = 3, which is a unit, inverse 25236.

(37853) divides n-1.

(37853)^2 > n.

n is prime by Pocklington's theorem.