Primality proof for n = 918583:

Take b = 2.

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

21871 is prime.
b^((n-1)/21871)-1 mod n = 627306, which is a unit, inverse 27156.

(21871) divides n-1.

(21871)^2 > n.

n is prime by Pocklington's theorem.