Primality proof for n = 372661:
Take b = 2.
b^(n-1) mod n = 1.
6211 is prime. b^((n-1)/6211)-1 mod n = 123811, which is a unit, inverse 297097.
(6211) divides n-1.
(6211)^2 > n.
n is prime by Pocklington's theorem.