Primality proof for n = 11783:

Take b = 2.

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

137 is prime.
b^((n-1)/137)-1 mod n = 1539, which is a unit, inverse 11538.

(137) divides n-1.

(137)^2 > n.

n is prime by Pocklington's theorem.