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.