Primality proof for n = 49290007066067:

Take b = 2.

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

10882031 is prime.
b^((n-1)/10882031)-1 mod n = 47170788343676, which is a unit, inverse 28702818375219.

(10882031) divides n-1.

(10882031)^2 > n.

n is prime by Pocklington's theorem.