Primality proof for n = 5779:

Take b = 2.

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

107 is prime.
b^((n-1)/107)-1 mod n = 2943, which is a unit, inverse 5671.

(107) divides n-1.

(107)^2 > n.

n is prime by Pocklington's theorem.