Primality proof for n = 214692087848261:

Take b = 2.

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

1114261 is prime.
b^((n-1)/1114261)-1 mod n = 58927038618951, which is a unit, inverse 86397854197348.

875803 is prime.
b^((n-1)/875803)-1 mod n = 195521985384770, which is a unit, inverse 82045486938931.

(875803 * 1114261) divides n-1.

(875803 * 1114261)^2 > n.

n is prime by Pocklington's theorem.