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.