Primality proof for n = 58480511:

Take b = 2.

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

2843 is prime.
b^((n-1)/2843)-1 mod n = 20458505, which is a unit, inverse 7163883.

17 is prime.
b^((n-1)/17)-1 mod n = 41217535, which is a unit, inverse 19680967.

(17 * 2843) divides n-1.

(17 * 2843)^2 > n.

n is prime by Pocklington's theorem.