- **Conjectures 'R Us**
(*https://www.mersenneforum.org/forumdisplay.php?f=81*)

- - **Bases 501-1030 reservations/statuses/primes**
(*https://www.mersenneforum.org/showthread.php?t=12994*)

[quote=KEP;168818]Hello
As part of my goal for this year, aswell in order to make sure my computer is not running idle while away on 3 weeks vacation some 4 weeks from now, I've decided to reserve 679 different Riesel bases with 1 thing in common, they all have k<=100K. All bases should be reported as completed in the end of this year. Also all bases will be tested to n=25K or proven. Already as I speak, 14 bases has been tested and 10 has been proven :smile: This also means, that the Sierp base 63 reservation will still run, though it will only run in idle mode, so during nighttime and awaytime from the computer, the Sierpinski base 63 reservation will get full attention. Hope that everyone is alright with this new approach :smile: Also I'll start by knooking down the riesel conjectures with the lowest predicted k-value. Regards KEP Ps. Will frequently return my output results to Gary, as more and more bases gets completely proven or tested to n=25K[/quote] All I can say is, good luck. You'll need it. For that many bases, it will take a large chunk of time just to show them on the pages and I don't want to spent an inordinate amount of time checking them. Therefore, I expect the following: 1. Remove all k's that are multiples of the base where k-1 is prime. 2. Remove all k's that contain algebraic factors, show which k's are removed, and show why they do in a manner at least somewhat consistent with my pages. You have to get the math down pat on this! You might check the algebraic factors thread to see the pattern of how many of them occur. 3. Analyze all bases that are perfect powers of smaller base(s). Check the k's for the smaller base(s) that have already been searched for primes and search limits. You may need to send Emails to me or to projects to find out about this. Example: Base 1024 will have primes that can be converted from bases 2 (perfect 10th power), 4, (perfect 5th power), and 32 (perfect square). This can get more complex than base 25. Kenneth, just pick 3-4 bases that have already been started and take them higher like I've done with bases 22 and 28 or Riesel bases 75 and 80. Alternatively like I've done with some of the Sierp bases < 100, take 3-4 bases at a time and take your time analyzing each one to make sure nothing is missed. Why continue choosing such humongous and difficult efforts? I don't get it. Gary |

1. There shouldn't be many k that are multiples of the base where k-1 is prime, since a majority of the larger k conjectures has high bases, hence multiplication will very fast make an conjectural overflow
2. Since not many k's will remain once I test further than n=2500, then srsieve will remove those with algebraic factors, and keep those k's that doesn't has algebraic factors, so that should also be possible to show which ones is removed as a result of algebraic factors. 3. This might be more complex, however I'll look into what I can do here, though I'm not strong on the math of that particular area. I did choose this, because I would really like to see someday that all base less than 2^10 has been taken to at least n=25K, and my personal goal was to see if this could be done for any bases where k<=100K before the end of 2009 :smile: So thats why plain and simple. Kenneth! [QUOTE=gd_barnes;168823]All I can say is, good luck. You'll need it. For that many bases, it will take a large chunk of time just to show them on the pages and I don't want to spent an inordinate amount of time checking them. Therefore, I expect the following: 1. Remove all k's that are multiples of the base where k-1 is prime. 2. Remove all k's that contain algebraic factors, show which k's are removed, and show why they do in a manner at least somewhat consistent with my pages. You have to get the math down pat on this! You might check the algebraic factors thread to see the pattern of how many of them occur. 3. Analyze all bases that are perfect powers of smaller base(s). Check the k's for the smaller base(s) that have already been searched for primes and search limits. You may need to send Emails to me or to projects to find out about this. Example: Base 1024 will have primes that can be converted from bases 2 (perfect 10th power), 4, (perfect 5th power), and 32 (perfect square). This can get more complex than base 25. Kenneth, just pick 3-4 bases that have already been started and take them higher like I've done with bases 22 and 28 or Riesel bases 75 and 80. Alternatively like I've done with some of the Sierp bases < 100, take 3-4 bases at a time and take your time analyzing each one to make sure nothing is missed. Why continue choosing such humongous and difficult efforts? I don't get it. Gary[/QUOTE] |

OK, suit yourself. Good luck.
What you are proposing would likely take a person with 2 quads many years and possible a decade or more to accomplish with current software at current computer speeds. But obviously I'm not going to convince you. When estimating things, which is required for setting realistic goals, you should take the most difficult task first, divide it up into as many smaller pieces as possible, and see how long all of those smaller pieces combined will take. Then determine how many tasks there are that are close to as difficult as the one that is most difficult, multiply that by the time to do the most difficult one, go on to "medium" difficult tasks, do the same, etc. Here is a thought: Find a base > 500 in your list that is not divisible by 3, is not b=2^q-1 (because those are the most prime), and that has a conjecture of k>~50000. See how long this base takes you to test it up to n=10000 and then report back how many k's are remaining, how long it will take to test that entire base up to n=25000, and how realistic your goal is. I am 100% sure that you will be unpleasantly surprised. Kenneth, I'm not going to keep responding trying to get you to reserve smaller and less difficult pieces of work. I've tried my best but for some reason, you simply refuse to take the time necessary to properly estimate things before reserving them. Srsieve will not remove k's that contain partial algebraic factors that make a full covering set. It will only tell you that you have SOME k/n pairs with algebraic factors that can be removed but that doesn't mean that ALL of the k/n pairs can be removed. The latter is a necessary condition for actually removing the k's from testing. Your statement about srsieve means that you clearly don't get the math. This is a math forum and this project can be quite math-intensive when starting new bases. I'll be glad to help you with the math involved but it has to be for a reasonable-sized reservation. I won't help at all with 674 bases, even if only 10-20 of them have k's with partial algebraic factors that make a full covering set. Sometimes I've spent up to 2 hours getting the algebraic factors correct on just one base. I've even found algebraic factors well after testing had gone on past n=25K, which wasted quite a bit of CPU time. After spending many hours at it, I've now generallized a lot of them (there's a thread about it) so it's not nearly as difficult to find them. That said, there are still many exceptions which pop up and are not easy to spot. Just report whatever you complete and I'll show it on my pages IF the work is correct. If it is not, I won't and will return it to you to fix it with only a cursory explanation. If you're going to reserve huge amounts of work, you have to get all of the work right with little assistance. If you're willing to be more realistic and reserve 3-4 bases at a time like everyone else does, I'll be glad to help you with some of the trickier ones. Only time will convince you how unrealistic your goal is. Gary |

@ Gary: OK, I'll still start up with the bases with the lowest k-values since they appear to be easily taken up to n=25K or even more easily proven. Since you're willing to allow me to not take the entire 679 bases to n=25K or proven, then I'll exclude all those bases where SRsieve tells me that there is partial algebraric factors. Doing it this way, most likely also means, that I'm not going to spend as much time working on the bases as I thought, and it might mean that I'm actually going to unreserve those bases that I've not computed any work on as soon as I return from vacation.
At the moment there is currently 33 proven bases where there is prime for all k's less than the conjectured k. However there will get to be loads more since there is still remaining conjectures with a conjectured lower k-value of 4. Aswell there is many with a lower conjectured k-value of 6 and 8 etc. However it can not be completely ruled out that some of these lower conjectures will be hard to take to n=25K, for their final remaining k. Kenneth |

[quote=KEP;168894]@ Gary: OK, I'll still start up with the bases with the lowest k-values since they appear to be easily taken up to n=25K or even more easily proven. Since you're willing to allow me to not take the entire 679 bases to n=25K or proven, then I'll exclude all those bases where SRsieve tells me that there is partial algebraric factors. Doing it this way, most likely also means, that I'm not going to spend as much time working on the bases as I thought, and it might mean that I'm actually going to unreserve those bases that I've not computed any work on as soon as I return from vacation.
At the moment there is currently 33 proven bases where there is prime for all k's less than the conjectured k. However there will get to be loads more since there is still remaining conjectures with a conjectured lower k-value of 4. Aswell there is many with a lower conjectured k-value of 6 and 8 etc. However it can not be completely ruled out that some of these lower conjectures will be hard to take to n=25K, for their final remaining k. Kenneth[/quote] Kenneth, Please read your Email. There are numerous problems with what you have sent me. I don't have time to review and fix everything before showing it on the pages so you need to correct it and send it back. After sending back the corrections, please stop this effort entirely and focus on bases 3 and 63. Base 63 by itself will take multiple CPU years to test to n=25K and so would easily keep your machines busy while you are gone. Heck, the sieving for n<131072 by itself should keep 8 cores busy for at least 3 weeks. It's simple enough to split up the P-ranges on multiple cores and tell srsieve to output factors in a manner similar to what sr2sieve does such that they can be removed from the main file. When you get back from your trip, then perhaps we can talk about specifically 3-5 bases that you can work on. If you finish those in 2 days, then we can do the same with another 3-5 bases. There's little reason to reserve so much at once, even if you do have big goals. Gary |

@ Gary: I've read your e-mail and replyed. I will follow your advice and leave the startups to someone who actually understands the basics.
Kenneth |

@ All:
I am unreserving my hundreds of Riesel reservations, since my computers is now guarenteed to be busy while on vacation, to someone else except the following Riesel base: 999 n=10000 (87 k's remaining) Regards Kenneth Ps. Following bases is proven (not yet send to Gary): 259, 519, 649, 714, 844 and base 989 has k=2 remaining at n=25K |

Kenneth,
Thanks for the udpate. Before I left on my last business trip 9 days ago, I updated the pages for many of your bases. I still have about 30 of them yet to list where the conjecture is k=4 and that you have proven. Since base 989 is not proven, can you please forward me your results file when you get back? Thanks, Gary |

Riesel Base 704Reserving Riesel Base 704 n=25K-40K
Riesel Base 704 complete from n=25K-40K - Nothing found Results emailed Riesel Base 704 released (Obviously I forgot to reserve it BEFORE I ran it, DUH) |

Below are some bases where b==(1 mod 30) with conjectures <=1000 that I've tested up to n=2500. I chose these because these are typically very primes bases for their size. A little over half were proven. More details are shown on the web pages.
Riesel base/conjecture/k's remain 571; k=12; proven 601; k=818; 50, 120, 300, 482, 624, & 744 781; k=254; 50 811; k=260; 8 & 258 901; k=12; proven 961; k=38; proven Sierp base/conjecture/k's remain 571; k=12; proven 601; k=216; proven 811; k=552; 252, 358, 378, 450, 510, & 538 901; k=12; proven 961; k=1000; 316, 508, 586, 630, 636, 688, 766, 778, 820, 846, 886, & 892 For now I'm not reserving any of these but I likely will later take the ones that have k's remaining to n=10K if other people haven't done so at that point. Gary |

50*781^3112-1 is prime!
I'll take Riesel 811 to 10k. Edit: k=8 has no primes to 10k, PFGWing k=258 now... |

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