Got it earlier today, thanks.
Got it earlier today, thanks.
Are you still looking for log files? I've got a few from just over a year ago, don't know how helpful they would be. Let me know if you could use them, and I'll do some digging to get them you.
We don't know which ones were double checked -- and at PrimeGrid I've got a really good window into the quality -- or lack thereof -- of the computers used in distributed computing. In general, we no longer trust any results unless they're double checked. The problem with not immediately double checking results is that when a computer starts going bad, you have no way of detecting it. So any results that don't have matching residues from different computers are suspect. Unless we get really lucky, except for whatever we can get from log files, we have no residues at all on 4 of the 6 k's.
Calculation errors are proportionally more likely to occur on larger candidates, especially when the error rate is fairly low, but non-zero.
Our position on double checking is especially rigid when it comes to conjectures like SoB. Consider a hypothetical k where the first prime is at n=100,000, and the second prime is at n=100,000,000. If you miss the first prime because of an undetected computation error, many years of unnecessary computing will be wasted searching for the second prime.
It's actually not as horrible as it might seem at first glance. The vast majority of candidates are small and can be rechecked much faster than the original search.
Unlike the Mersenne prime search, we only need to double check positive results. The time double-checking is better spent checking new numbers. For Mersenne primes, we want a complete list. For 17-or-bust, we only need to find a prime for each coefficient. If we get a false negative, no harm is done if we find a prime for that coefficient.