Primality proof for n = 1684996666696914987166688442938727098634905596057513265952429863687:

Take b = 2.

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

842498333348457493583344221469363549317452798028756632976214931843 is prime.
b^((n-1)/842498333348457493583344221469363549317452798028756632976214931843)-1 mod n = 3, which is a unit, inverse 561665555565638329055562814312909032878301865352504421984143287896.

(842498333348457493583344221469363549317452798028756632976214931843) divides n-1.

(842498333348457493583344221469363549317452798028756632976214931843)^2 > n.

n is prime by Pocklington's theorem.