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.