Primality proof for n = 11201767:
Take b = 2.
b^(n-1) mod n = 1.
1866961 is prime. b^((n-1)/1866961)-1 mod n = 63, which is a unit, inverse 4089534.
(1866961) divides n-1.
(1866961)^2 > n.
n is prime by Pocklington's theorem.