Primality proof for n = 49603261419390422248082736481:

Take b = 2.

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

188642800889 is prime.
b^((n-1)/188642800889)-1 mod n = 22369571355841450008810717338, which is a unit, inverse 37353789587814669127920530490.

11799461 is prime.
b^((n-1)/11799461)-1 mod n = 30004165016407962499294149411, which is a unit, inverse 17981385831873780732865201666.

(11799461 * 188642800889) divides n-1.

(11799461 * 188642800889)^2 > n.

n is prime by Pocklington's theorem.