Ok, so you just use that particular algorithm to generate random numbers. Have you studied how many % of large random numbers meet your expectations? And what will happen when you hit actual prime or composite that has only relatively small factors? There will be lot of them.
Great questions keep them coming! Originally I was worried about primes but one of the other posters alerted me that everyone can be working on different numbers. I didn't realize this is how bitcoin works currently. Everyone's number is determined by the hash of their public key along with other block details. So if one person gets dealt a prime (or two or three or 100 people) then the others will be the ones to win that block. This is kind of good because the winning number we know are not prime, so if certain numbers aren't showing up in our list of winning numbers, we can say they may be prime.
So at this size, there will be primes I'm guessing 1 out of 5,000 numbers. So not bad at all, pretty much inconsequential for the network as a whole. Lets say we are looking for 20 digit factor of a 100 digit number. This is like saying we are looking for a 2 digit factor (12 for example) of a 10 digit number (2,000,000,000 for example) so they should be very very common. Really since everyone generates their own numbers it doesn't even matter how common a working number will be. We just need one person to find a match.