Primality proof for n = 187019741:
Take b = 2.
b^(n-1) mod n = 1.
9350987 is prime. b^((n-1)/9350987)-1 mod n = 1048575, which is a unit, inverse 44930397.
(9350987) divides n-1.
(9350987)^2 > n.
n is prime by Pocklington's theorem.