Primality proof for n = 49712609355733181957277501974736893:

Take b = 2.

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

719569513687 is prime.
b^((n-1)/719569513687)-1 mod n = 3682321743096489226585743440975125, which is a unit, inverse 26510255626462026520920073970749131.

151499460061 is prime.
b^((n-1)/151499460061)-1 mod n = 48671800463545980605052623112158222, which is a unit, inverse 27928040730318928714495288851105246.

(151499460061 * 719569513687) divides n-1.

(151499460061 * 719569513687)^2 > n.

n is prime by Pocklington's theorem.