Primality proof for n = 97859369123353:

Take b = 2.

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

379979 is prime.
b^((n-1)/379979)-1 mod n = 94986100431262, which is a unit, inverse 41608912195100.

271 is prime.
b^((n-1)/271)-1 mod n = 93325906734243, which is a unit, inverse 24193097608682.

(271 * 379979) divides n-1.

(271 * 379979)^2 > n.

n is prime by Pocklington's theorem.