Primality proof for n = 83287801:

Take b = 2.

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

46271 is prime.
b^((n-1)/46271)-1 mod n = 67896832, which is a unit, inverse 50237570.

(46271) divides n-1.

(46271)^2 > n.

n is prime by Pocklington's theorem.