Primality proof for n = 90263:

Take b = 2.

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

45131 is prime.
b^((n-1)/45131)-1 mod n = 3, which is a unit, inverse 30088.

(45131) divides n-1.

(45131)^2 > n.

n is prime by Pocklington's theorem.