Primality proof for n = 35796097:
Take b = 2.
b^(n-1) mod n = 1.
193 is prime.
b^((n-1)/193)-1 mod n = 19766568, which is a unit, inverse 14942612.
23 is prime.
b^((n-1)/23)-1 mod n = 25868511, which is a unit, inverse 16542853.
7 is prime.
b^((n-1)/7)-1 mod n = 14510439, which is a unit, inverse 3237157.
(7 * 23 * 193) divides n-1.
(7 * 23 * 193)^2 > n.
n is prime by Pocklington's theorem.