Primality proof for n = 3100695749:

Take b = 2.

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

3016241 is prime.
b^((n-1)/3016241)-1 mod n = 2571865143, which is a unit, inverse 2840982649.

(3016241) divides n-1.

(3016241)^2 > n.

n is prime by Pocklington's theorem.