Primality proof for n = 6730519843040614479184435237013:

Take b = 2.

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

8464734851 is prime.
b^((n-1)/8464734851)-1 mod n = 3681886084939357546404908796125, which is a unit, inverse 3039756709910638621157556372474.

671065561 is prime.
b^((n-1)/671065561)-1 mod n = 5255658239705769014805159091582, which is a unit, inverse 3086872343501381515492565796044.

(671065561 * 8464734851) divides n-1.

(671065561 * 8464734851)^2 > n.

n is prime by Pocklington's theorem.