Primality proof for n = 49081234303:

Take b = 2.

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

3878713 is prime.
b^((n-1)/3878713)-1 mod n = 34242322587, which is a unit, inverse 18864062710.

(3878713) divides n-1.

(3878713)^2 > n.

n is prime by Pocklington's theorem.