Primality proof for n = 35537:

Take b = 2.

b^(n-1) mod n = 1.

2221 is prime.
b^((n-1)/2221)-1 mod n = 29998, which is a unit, inverse 19273.

(2221) divides n-1.

(2221)^2 > n.

n is prime by Pocklington's theorem.