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.