Primality proof for n = 37997:
Take b = 2.
b^(n-1) mod n = 1.
59 is prime.
b^((n-1)/59)-1 mod n = 4997, which is a unit, inverse 37229.
23 is prime.
b^((n-1)/23)-1 mod n = 26633, which is a unit, inverse 37131.
(23 * 59) divides n-1.
(23 * 59)^2 > n.
n is prime by Pocklington's theorem.