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.