Primality proof for n = 10748006189:
Take b = 2.
b^(n-1) mod n = 1.
121271 is prime. b^((n-1)/121271)-1 mod n = 2683161203, which is a unit, inverse 3580907642.
(121271) divides n-1.
(121271)^2 > n.
n is prime by Pocklington's theorem.