Brief answers
1. There are ways to prove a number is prime without factoring.
For example, Selfridge and Hurwitz showed that 14th Fermat number
was composite in 1963, but no one knows any of the divisors to this day.
(It is a really big number. They call it F14.)
2. Ecker primes, are found by first selecting random numbers of the size needed, and then checking to see if it is prime. (For 100digit primes the chance is about 8+ in 1000 are prime using the Ecker prime method. About .4% of 100digit numbers are prime.
3. Even if you know a 200 digit is made of two 100digit primes, it would still take a long time (and a bit of effort) to factor it.
4. Generally speaking, a number cannot be copyrighted. Neither can a list of numbers.
