20121004, 03:42  #78  
"Phil"
Sep 2002
Tracktown, U.S.A.
3·373 Posts 
Quote:


20121004, 05:53  #79 
Jun 2003
2^{4}·5·67 Posts 

20121004, 05:55  #80 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011011101010_{2} Posts 
Sorry for the delay, no free time, I just found a bit of time during lunch break but I could not access the computer (remoting to my house, I think out IT dept did something with the firewall or the servers during the lunch).
Now I got it. The k's which were eliminated in my table were: Code:
#34: 1257787: k = 149,249,504,600,785,872 #35: 1398269: k = 180,240,248,273,609,849 #36: 2976221: k = 56,528,996 #37: 3021377: k = 81,333,420,608,660 #38: 6972593: k = 68,185,336,369,453,741,884,956 #39: 13466917: k = 69,93,96,476,576,653,953 #40: 20996011: k = 113,272,657,740 #41: 24036583: k = 113 #42: 25964951: k = 164,473,657,713,893,944 #43: 30402457: k = 176,261,273,288,641,744 #44: 32582657: k = 44,221,273,453,489,576,720,944,980 #45: 37156667: k = 524,693,713,944 #46: 42643801: k = 44,221,393,428,744 #47: 43112609: k = none Code:
#34,149 has a factor : 306852607 #34,249 has a factor : 41338111 #34,504 has a factor : 91596737 #34,600 has a factor : 135549677 #34,785 has a factor : 57979847 #34,872 has a factor : 370969009 #35,180 has a factor : 452535697 #35,240 has a factor : 150051247 #35,248 has a factor : 60082859 #35,273 has a factor : 234717979 #35,609 has a factor : 585942169 #35,849 has a factor : 352875203 #36, 56 has a factor : 147547391 #36,528 has a factor : 41221249 #36,996 has a factor : 646207649 #37, 81 has a factor : 76165591 #37,333 has a factor : 427066817 #37,420 has a factor : 411433669 #37,608 has a factor : 33456589 #37,660 has a factor : 809870977 #38, 68 has a factor : 34411649 #38,185 has a factor : 386501543 #38,336 has a factor : 439589651 #38,369 has a factor : 738469559 #38,453 has a factor : 36832979 #38,741 has a factor : 896870687 #38,884 has a factor : 45868327 #38,956 has a factor : 58198181 #39, 69 has a factor : 119370001 #39, 93 has a factor : 33674209 #39, 96 has a factor : 194242183 #39,476 has a factor : 203942419 #39,576 has a factor : 307063187 #39,653 has a factor : 333708901 #39,953 has a factor : 565776451 #40,113 has a factor : 33208589 #40,272 has a factor : 227322647 #40,657 has a factor : 33082001 #40,740 has a factor : 108790961 #41,113 has a factor : 492502253 #42,164 has a factor : 168153533 #42,473 has a factor : 47613217 #42,657 has a factor : 67042249 #42,713 has a factor : 88283473 #42,893 has a factor : 601958087 #42,944 has a factor : 60004817 #43,176 has a factor : 72848761 #43,261 has a factor : 127585477 #43,273 has a factor : 297084287 #43,288 has a factor : 193964599 #43,641 has a factor : 542210323 #43,744 has a factor : 479934337 #44, 44 has a factor : 415021787 #44,221 has a factor : 77249351 #44,273 has a factor : 994172791 #44,453 has a factor : 120304357 #44,489 has a factor : 138744079 #44,576 has a factor : 33481247 #44,720 has a factor : 231810473 #44,944 has a factor : 101857159 #44,980 has a factor : 220184941 #45,524 has a factor : 53040683 #45,693 has a factor : 232066663 #45,713 has a factor : 177675227 #45,944 has a factor : 101350111 #46, 44, tested to : 1000000007, no factor. #46,221 has a factor : 161362987 #46,428 has a factor : 514204841 #46,744 has a factor : 85648273 #46,393 has a factor : 421524893 
20121004, 07:14  #81 
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}·7·173 Posts 
Nice job, folks, thank you very much!
The DB for this search is ready, I will work out some online tables during the weekend (or even earlier, if I find time), so that everyone will have a clear idea of who is doing what at which level... @Ernst, thank you for the ks; your software is great as is, no need to continue sieving after a factor is found. @Phil, thank you for the information about your sieving work. @LaurV, M#42 and M#46 have been checked up to 10G, five k have been cleared, I collected the factors for doublechecks. M#47 is being taken to 1T. I am attaching your table with my extensions here, please confirm or correct your claimed ranges . I will work on automatic reservation system as I get started with the tables management. BTW, any ideas for a name of this sieving project? Luigi Last fiddled with by ET_ on 20121004 at 07:16 
20121004, 09:55  #82 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
236_{16} Posts 
Some basic questions
I am following this discussion with great interest. Sorry for draging it down to a basic level and at the same time exploring my ignorance , so if I may I would like to ask a few basic questions, just making sure that I have understood what it is all about,
1. So what you are doing right now is to sieve to find possible candidates that might divide the very large double mersennes MM#34  MM#47. What you find is possible candidates that might divide MM#34  MM#47 respectively. Is that rignt? 2. So when you are speaking of "factors" you are not speaking of factors of the double mersennes but factors of the possible candidates which have the form 2*k*[M#34M#47]+1 for different k:s. Is that right? So it is rather factors of possible factors and these factors of factors do not have any special form known? 3. And the reason why you are not using the candidates found for TF of MM#34MM#47 is that these numbers are so increadibly large that, presently there is no program available that could do such a TF. Is that right? 4. And if you find a factor of MM#47 that factor would be larger then M#47 hence the largest prime found? Is that right? Once again sorry for asking these basic questions! 
20121004, 10:08  #83  
Romulan Interpreter
"name field"
Jun 2011
Thailand
26EA_{16} Posts 
Quote:
i.e. to LL any M_{p} (the job we normally do for GIMPS), you start with s_{0}=4 and do s_{n+1}=s_{n}^{2}2 (mod M_{p}), p2 times otoh, to test if 2*k*M_{p}+1 divides MM_{p}, you start with s_{0}=2 and do s_{n+1}=s_{n}^{2} (mod 2*k*M_{p}+1), exactly p times (so there are two more iterations), and the mod is just few bits (for a small k) bigger then M_{p} (taking about the same time, in fact). The time will be the same like doing LL test for exponent p (about). Last fiddled with by LaurV on 20121004 at 10:18 

20121004, 10:31  #84 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×17×293 Posts 
A small observation about question 4 (deliberately a separate post, do be easy visible, and not lost in the TL;DR text of the former post):
If we find a factor q=2*k*M#47+1 of MM#47, for such a small k [in fact for ANY k smaller than or equal to (M#47+2)], that number q will be higher then 2*M#47+1 (in fact, larger than, or equal to 2*185*M#47+1). And that factor q will be PRIME. And it will be for the first time in a VERY LONG history when the LARGEST KNOWN PRIME is not a mersenne number. Last fiddled with by LaurV on 20121004 at 10:47 
20121004, 10:59  #85 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
566_{10} Posts 

20121004, 13:32  #86  
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}·7·173 Posts 
Quote:
Luigi 

20121004, 18:45  #87  
∂^{2}ω=0
Sep 2002
República de California
3^{2}×1,303 Posts 
Quote:
Also note  and I don't mean to damp folks' enthusiasm here, just to set realistic expectations  that for the kinds of M(Mp) we're discussing here, the fact that a given candidate q has no factors below (say) 10^15 or even ~10^20 (probabilistically, if one follows the TF with p1 and/or ecm) only slightly increases the odds of q being prime, from [a very small number] to perhaps 2 or 3 times [a very small number]. Of course such a find would be spectacular, and one does not improve the methods available for attempting such a feat by giving up because the odds seem to be so daunting. One can learn much from failed attempts, if one approaches such projects from an algorithmicimprovement perspective, rather than one of "my life will only have meaning if this succeeds".  p.s. to Luigi: My run of MM#47(k=185) is to 10T, not 1T. (97% complete as I write this, odds of finding a factor in the final 3% very small). If folks want to do this one very deeply, I suggest divvying up the range 10100T into 9 10Tsized chunks and handing those out to people interested in asssigning 1 or more CPU to the task. 

20121004, 19:11  #88  
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}×7×173 Posts 
Quote:
The idea was indeed to take the first 1000 k that survive lowlevel sieving to (say) 1T, and then dedicate resources to deepsieving the first candidate of each row (exponent), in the hope of enhancing our knowledge about the limits of these ranges. The idea of using 9 ranges of 10T to get to 100T is nice, but risky: if you dedicate your hardware to test 40T100T, you would not be happy when I will tell you that the factor was hidden on the 10T20T range. A different approach could be testing the first candidate of each exponent in parallel to minimize the risk, but then we may not find a record nonMersenne prime. Anyway, I don't think there will be much audience for this project, and my worries may as well disappear. Said from the one who launched the Operation Billion Digits with William Lipp. On another thought, without OBD we would not have had mfaktc... Luigi Last fiddled with by ET_ on 20121004 at 19:11 

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