Primality proof for n = 387610748845807843:

Take b = 2.

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

3462603391451 is prime.
b^((n-1)/3462603391451)-1 mod n = 95092123335069277, which is a unit, inverse 64717415888666420.

(3462603391451) divides n-1.

(3462603391451)^2 > n.

n is prime by Pocklington's theorem.