Question about OPN sieving
I thought of a random question today about the process of sieving of odd perfect numbers. As I have understood the process, we take prime numbers less than an arbitrary limit and generate sigma chains based on powers of those prime numbers. It occurred to me that we can't possibly check the sigma chains on ALL the primes less than the limit, so I now have two questions:
1. Since we can't check them all, how do we know that we've eliminated all possible OPNs below 10^2000 or whatever other limit we have chosen?
2. How do we pick the right prime numbers to start the sigma chains?
