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.