Primality proof for n = 641:
Take b = 3.
b^(n-1) mod n = 1.
5 is prime.
b^((n-1)/5)-1 mod n = 356, which is a unit, inverse 632.
2 is prime.
b^((n-1)/2)-1 mod n = 639, which is a unit, inverse 320.
(2^7 * 5) divides n-1.
(2^7 * 5)^2 > n.
n is prime by Pocklington's theorem.