Primality proof for n = 649570254101:

Take b = 2.

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

6495702541 is prime.
b^((n-1)/6495702541)-1 mod n = 139302284203, which is a unit, inverse 314279758245.

(6495702541) divides n-1.

(6495702541)^2 > n.

n is prime by Pocklington's theorem.