My understanding is that the algorithm to find primes works on all numbers, not one at a time. Simplified it goes like this:
Pick an upper limit of digits that will be the ceiling.
Take the first prime number (2). Find all of its products up to the ceiling you've decided on.
Take the first number not in the above set of products (3) which will also be prime. Find all of its products up to the ceiling.
Do this with the first number not in any of the product lists (5, 7, 11, 13, 17, 19, 23, etc) in succession. When you hit a nonproduct number greater than the greatest known prime, you've got a new prime.
I guess you could start analyzing a single prime number by reversing the process, but you'd still have to do all the calculations starting with a number that is 1/2 the prime. So I guess you could analyze 2 bought primes for the value of finding your own.
