Primality proof for n = 37409:
Take b = 2.
b^(n-1) mod n = 1.
167 is prime.
b^((n-1)/167)-1 mod n = 23542, which is a unit, inverse 27441.
7 is prime.
b^((n-1)/7)-1 mod n = 26260, which is a unit, inverse 29846.
(7 * 167) divides n-1.
(7 * 167)^2 > n.
n is prime by Pocklington's theorem.