Primality proof for n = 60934327561511008916380516463943361:

Take b = 2.

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

289450259140102639080071069 is prime.
b^((n-1)/289450259140102639080071069)-1 mod n = 22503414753582025559838584699846658, which is a unit, inverse 55855394240861195045502250692151378.

(289450259140102639080071069) divides n-1.

(289450259140102639080071069)^2 > n.

n is prime by Pocklington's theorem.