Primality proof for n = 3678475954780960471:

Take b = 2.

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

78751358483857 is prime.
b^((n-1)/78751358483857)-1 mod n = 3448234981816859156, which is a unit, inverse 235776575702676806.

(78751358483857) divides n-1.

(78751358483857)^2 > n.

n is prime by Pocklington's theorem.