1) Message boards : Extended Sierpinski Problem : k = 202705 (Message 152533) Posted 360 days ago by dukebg The question is, will new factors always be able to periodically fill a specific fraction of the holes? I guess the possibility is always there, so it might turn into a Sierpinski number. I hope it's clear what I meant. That's actually an easy question to answer. If a number k*b^n+1 has a prime factor q then rearranging you get b^n = -1*inverse(k) (mod q). The right side is a constant. Obviously, this will be true for any n(m) = n + G * m, where m is any integer and G is the group order of b – i.e. the period of the sequence b(n) = b^n (mod q). In other words, every factor that you find for a number of form k*b^n+1 is always a factor for an infinite amount of these numbers – their series of n's form an arithmetic progression. That's basically how you construct the covering sets for these numbers. You get a set of primes whose group orders line up nicely inside a least common multiple and you adjust the K to have each of them cover different remainders. And even if you find a "k*b^n+1" number that is a prime itself – it itself is a factor for a series of further n's. The difference in that series would be the group order of b in (mod k*b^n+1) Back to the question, the problem is whether or not all these covering arithmetic progressions will cover everything. Well, as prime grows arbitrary bigger, the group orders grow arbitrary bigger too. And if you aim to cover all remainders with some target LCM that I mentioned above, there's only a finite amount of them – it's easy to show all of them have to be factors of b^LCM - 1. So you constantly have to move into bigger and bigger territories. And all primes that you find have to be included in the covering set and boost the "target LCM" to a ridiculous degree So yeah, maybe with a 6-million digit prime there would be a covering set for all the larger numbers. But it will likely include a 6-million digit number of entries in the covering set. 2) Message boards : Number crunching : Once in a Blue Moon Challenge (Message 151187) Posted 472 days ago by dukebg Why is the abortion-rate that high? I mean, i too aborted around 10 %, to "realign" the WUs with some DC-tasks, but that high a percentage? Any ideas? There are many scenarios in which you download more tasks than you actually want to run and abort some of them – maybe by some logic. Some of them were outlined by others above, but I'ld like to point out one more. There's a bug in BOINC where – if you don't have any tasks for some subproject in your client_state.xml or whatever and you start running that subproject, it will download one task per each core (as if you were going to run one task per core), independent of the settings of how many cores per task you've set for the subproject. So it's very possible to get way too many tasks downloaded at the start of the challenge like this and abort most of them. Maybe this was fixed or alleviated by the changes with how you can set multi-threading from the server side preferences now, I wouldn't know for sure (haven't crunched in... years now). 3) Message boards : Seventeen or Bust : Seventeen or Bust and the Sierpinski Problem (Message 149355) Posted 631 days ago by dukebg I'm a bit surprised the GIMPS news item has only appeared now. It was implemented there in fall last year already (see the dates for the last assignments here for an example). I guess the most important point of writing about this in the news was to prompt users to update to the new version because the old one will no longer be used for first time tests from some point. But yeah, all of this started by Pavel on PrimeGrid developing a general certification scheme, then Preda (mentioned in the news) from GIMPS forums suggested the Pietrzak's function, Pavel (together with stream and other PG admins) deployed the final implementation here (called LLR2), George was working on implementing it in GIMPS and Pavel helped there by described the scheme, what nuances and pitfalls there are (in regards to preventing cheating, etc). And then it was out in GIMPS too. 4) Message boards : The Riesel Problem : K = 192971 prime found by Propper (Message 149302) Posted 632 days ago by dukebg Unless I'm misunderstanding https://www.primegrid.com/stats_trp_llr.php this range should not conflict with Primegrid - now or for a while? For a while, yes. PG has TRP k's fully sieved to n=50M according to this old post. The stats page shows the candidates currently "loaded" into the system and more are loaded from the sieve file periodically. Unless something happens, PG plans (as far as I'm aware) are to search each k until a prime is found or to the end of the sieve file (50M). This is, of course, a 10+ years plan. EDIT: I'm pretty sure, if there is outside interest to run some of the K's externally with large resources and not have PG do work on them, PG admins could agree to some sort of arrangements of this kind. 5) Message boards : Seventeen or Bust : Are people even sure 78557 is the smallest k? (Message 140243) Posted 932 days ago by dukebg A more on-topic message. I started typing a message about why would the covering set from the dual problem automatically become a covering set in the "non-dual" problem. But then I figured it out on my own. Fun math. 6) Message boards : Seventeen or Bust : Are people even sure 78557 is the smallest k? (Message 140241) Posted 932 days ago by dukebg Ravi Fernando wrote:So e.g. k=67607 is known to produce at least two primes (or maybe PRPs, not sure if they've been tested with ECPP): 2^16389 + 67607 and 2^46549 + 67607. It appears the first of these two numbers was proven prime just 2 months ago: http://factordb.com/index.php?id=1100000000537223829. Oh, that was most likely a lucky happenstance. Masaki UKAI runs ECPP basically for all PRPs in FDB of that size. 4.9K dd is pretty small, just few hours on modern hardware. I don't think they ran this exact number on purpose. 7) Message boards : Generalized Fermat Prime Search : GFN-16 MEGA Prime Search starts March, 14, 2019 (Message 139718) Posted 958 days ago by dukebg I thought we were already in the cleanup since the finds. 8) Message boards : General discussion : Potential for cheap supercomputer array for PrimeGrid (Message 133114) Posted 1167 days ago by dukebg This would be great for people who want to help but can't directly volunteer their machines and would rather donate directly. They could just... donate directly then. 9) Message boards : General discussion : Encryption / Cybersecurity (Message 133113) Posted 1167 days ago by dukebg My main intention with PrimeGrid is to help bolster cybersecurity. Does anyone have any recommendations for which subprojects are most likely to discover primes useful for encryption? Thanks! absolutely none. 10) Message boards : Project Staging Area : multiple jobs assigned to single processors (Message 132572) Posted 1184 days ago by dukebg Or is the problem that the server thinks it sent more than one task to you, but you only have one of the tasks on your computer? If that's the problem, just ignore it. Only the tasks actually received by your computer will be run on your computer, and the others will time out and then be sent out again. This, but it happened for everybody who received tasks at that time.

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