Primality proof for n = 59180993314580506221962671096753:

Take b = 2.

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

1779835204363103 is prime.
b^((n-1)/1779835204363103)-1 mod n = 40080469633070974444189506270939, which is a unit, inverse 1757613885766652203934927546444.

352173651449 is prime.
b^((n-1)/352173651449)-1 mod n = 40708056726482894591915319627626, which is a unit, inverse 55146929872946558300027028079362.

(352173651449 * 1779835204363103) divides n-1.

(352173651449 * 1779835204363103)^2 > n.

n is prime by Pocklington's theorem.