Primality proof for n = 11594917:

Take b = 2.

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

103 is prime.
b^((n-1)/103)-1 mod n = 2141068, which is a unit, inverse 7613167.

59 is prime.
b^((n-1)/59)-1 mod n = 4708379, which is a unit, inverse 5437502.

(59 * 103) divides n-1.

(59 * 103)^2 > n.

n is prime by Pocklington's theorem.