Primality proof for n = 214824846426985860661:

Take b = 2.

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

19505309445451 is prime.
b^((n-1)/19505309445451)-1 mod n = 210993610960317807170, which is a unit, inverse 37139972704204312855.

(19505309445451) divides n-1.

(19505309445451)^2 > n.

n is prime by Pocklington's theorem.