Primality proof for n = 1135613:
Take b = 2.
b^(n-1) mod n = 1.
1471 is prime. b^((n-1)/1471)-1 mod n = 741221, which is a unit, inverse 1043786.
(1471) divides n-1.
(1471)^2 > n.
n is prime by Pocklington's theorem.