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.