Primality proof for n = 5962933401120092733206902139:

Take b = 2.

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

1841796684943080163 is prime.
b^((n-1)/1841796684943080163)-1 mod n = 380436305937954296774012571, which is a unit, inverse 90283593031434204813586420.

(1841796684943080163) divides n-1.

(1841796684943080163)^2 > n.

n is prime by Pocklington's theorem.