Primality proof for n = 3059213862715144055733503214373292934438943635608167530247:

Take b = 2.

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

49712609355733181957277501974736893 is prime.
b^((n-1)/49712609355733181957277501974736893)-1 mod n = 615606531395377963789753003177189735540278635466750652952, which is a unit, inverse 2000647132246386634968649860158340056061571700086071238254.

(49712609355733181957277501974736893) divides n-1.

(49712609355733181957277501974736893)^2 > n.

n is prime by Pocklington's theorem.