Primality proof for n = 101:

Take b = 2.

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

5 is prime.
b^((n-1)/5)-1 mod n = 94, which is a unit, inverse 72.

(5^2) divides n-1.

(5^2)^2 > n.

n is prime by Pocklington's theorem.