Primality proof for n = 359799907329331097897:
Take b = 2.
b^(n-1) mod n = 1.
107338874501590423 is prime.
b^((n-1)/107338874501590423)-1 mod n = 279454942371915157254, which is a unit, inverse 304334135652787504710.
(107338874501590423) divides n-1.
(107338874501590423)^2 > n.
n is prime by Pocklington's theorem.