Primality proof for n = 1279:

Take b = 2.

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

71 is prime.
b^((n-1)/71)-1 mod n = 1227, which is a unit, inverse 1156.

(71) divides n-1.

(71)^2 > n.

n is prime by Pocklington's theorem.