## Other

drummers-lowrise
 1) Message boards : Seventeen or Bust : Are people even sure 78557 is the smallest k? (Message 140178) Posted 499 days ago by wolfemancs It was kind of hinted at in one of the previous replies, but I think it's worth pointing out (and it's probably covered better than I can in one of the links). The reason we know 78557 is a Sierpinski number is that it has been shown to have a so called "Covering Set"; a set of small primes that it can be shown with modular arithmetic to evenly divide k*2^n+1 for every n. (I think there are 19 of the primes, and it can be shown that if n/18 has remainder zero, this prime divides, 78557*2^n+1, and if n/18 has remainder 1, this other prime divides 78557*2^n+1, and so on for all 19 possible remainders of n/18) All known Sierpinski numbers have a fairly small covering set. All the ks remaining in SoB have been proven to NOT have a covering set of any size. So the fact that we know they don't have a covering set gives us a little bit of hope that there will eventually be a prime for each of the remaining k. This is all from memory of reading up on this 5-10 years ago... so please anyone who knows better feel free to correct my statements. 2) Message boards : Picard message board (Message 130834) Posted 813 days ago by wolfemancs I'm still lurking, and reading the forums, but I haven't been crunching lately. 3) Message boards : Number crunching : 2019 Tour de Primes (Message 126230) Posted 961 days ago by wolfemancs And back to the original discussion. No, there is not a fixed number of primes in a given interval... Ah, silly English not being specific enough to indicate a single meaning unless 10,000 words are used. :) What I meant by "given interval" was a specific one. In the interval [1,10] there are 4 primes. So if you were to manage to be the 1st finder for every task in that interval, you'd find all 4. (understanding now that it's not possible to get all the tasks. just clarifying language) I didn't mean to imply that the next interval of the same size [11,20] would have the same number of primes, but I can see how it could be read that way. (ok.... it DOES also contain 4 primes, my examples suck.) 4) Message boards : Number crunching : 2019 Tour de Primes (Message 126223) Posted 961 days ago by wolfemancs What the others do has no influence on the probability of finding a prime. These are independent random events. There is a fixed number of primes in a given interval. The more PPSE are being processed, the larger the interval, but the smaller is your proportion of searching it. 10 times as many PPSE processed, 10 times as many primes. The chance of finding one in that interval is 10 times higher, but the chance that you will be the one to find it is 10 times smaller. So I guess you are correct and the probability remains the same. For us plebs, I think this is true. But at the extreme it might not be... (if you define finding a prime as being the first finder) If, for example, someone with the computing power that was lent to us to close out that one sieve project was turned onto PPSE while an SGS challenge was going on, they might easily pass 50% of the total work being done on PPSE. If (assumption made here) the scheduler sends out the smallest work unit available, then a single user doing more than 50% of the work, would increase the n they are working on faster than double checkers could keep up. This would lead to the super user finding ALL the primes in the interval. And while each task (within a reasonable size range) has the same probability of being prime, this guarantees that no one else ever finds a prime, so intuitively, while you might find primes at the same rate, you end up with more. (and are never a double checker because you're always getting the first task). If someone decides this is a useful strategy, and would like to hire a server farm to implement it, as a finder's fee for finding this strategy for you, I would ask that you use the farm on my favorite project, SoB. ;-) 5) Message boards : General discussion : Favourite Prime Number. (Message 124324) Posted 992 days ago by wolfemancs Yeah I have a fondness for oxymorons that sound more plausible on account of the obscurity of the words. "Sceptical omphalist" would be another example. If you have a fondness for sphenic numbers, the wikipedia page for them needs updating. They have the largest sphenic number known as of Jan of 2018, but there's a new biggest prime since then. 6) Message boards : General discussion : Boink vs Bo Inc (Message 122518) Posted 1042 days ago by wolfemancs You could end all debate and simply call it Berkeley Open Infrastructure for Network Computing. Ber-Key-Lee ? Berk-Elee ? Berkeh-Lee ? Nah. We American's are fans of the silent e, and we like to put it where ever we want. BURK-lee (could be BERK.... hard to differentiate the two to me.) 7) Message boards : Number crunching : Oktoberfest Challenge (Message 120599) Posted 1099 days ago by wolfemancs "No primes yet!" removed from the bottom of the daily summary post...... oversight? or . . . . . . . . . . . . . 8) Message boards : Number crunching : World Cup Challenge (Message 118669) Posted 1195 days ago by wolfemancs Russia 5 Saudi Arabia 0 What a good start to the Tournament. Russia played well, and Saudis outclassed. Makes you wonder how the Aussies will fair against France & Denmark. But everyone likes goals. :-) Gah! I can't even come to a MATH website w/o spoilers??? I knew I had to avoid ESPN, but PrimeGrid? j/k (mostly) 9) Message boards : Number crunching : World Cup Challenge (Message 118653) Posted 1196 days ago by wolfemancs Question about SR5: Why are we looking specifically at EVEN base 5 Sierpinski/Riesel numbers? Is it so LLR and Proth tests work? Are we using the 5^[huge number] as the k and testing 2^[small number]? 10) Message boards : The Riesel Problem : TRP Double Check (Message 118166) Posted 1217 days ago by wolfemancs Does anyone involved know what the acceptable error rate was to have Adaptive Replication turned on for a client? I wonder how close the 0.1-0.5% error rate compares to the error rate that was expected for computers that were "trusted" by the Adaptive Replication process.

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