Primality proof for n = 140977:

Take b = 2.

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

89 is prime.
b^((n-1)/89)-1 mod n = 71723, which is a unit, inverse 116710.

11 is prime.
b^((n-1)/11)-1 mod n = 57131, which is a unit, inverse 55309.

(11 * 89) divides n-1.

(11 * 89)^2 > n.

n is prime by Pocklington's theorem.