Primality proof for n = 486612738928707810813763:

Take b = 2.

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

390024685630946447 is prime.
b^((n-1)/390024685630946447)-1 mod n = 225226047209282553645728, which is a unit, inverse 403708468608367048550267.

(390024685630946447) divides n-1.

(390024685630946447)^2 > n.

n is prime by Pocklington's theorem.