Primality proof for n = 67954897631837:

Take b = 2.

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

4565634079 is prime.
b^((n-1)/4565634079)-1 mod n = 63117859452440, which is a unit, inverse 9505975051969.

(4565634079) divides n-1.

(4565634079)^2 > n.

n is prime by Pocklington's theorem.