20100112, 19:53  #1 
"Mark"
Apr 2003
Between here and the
1830_{16} Posts 
Conjectures with one k remaining
I thought it would be interesting to list the conjectures with 1 k remaining to see if anyone would be willing to take the k in an effort to solve the conjectures. Obviously a bunch are reserved, but quite a few look ripe for the picking at 25K. I would take some myself, but I need to finish some of the work I currently have before I take on more. Clearly there are some huge primes out there waiting for someone to get lucky.
*  sieve file available Sierpinski Conjectures: Code:
test reservation/ form weight limit comments 2036*9^n+1 502 5M 7666*10^n+1 263 3.06M Cruelty 244*17^n+1 334 5M 5128*22^n+1 534 2M* 398*27^n+1 799 2M* 166*43^n+1 928 1M* 17*68^n+1 988 1M* 1312*75^n+1 221 1.3M* 8*86^n+1 848 1M* 32*87^n+1 342 1M* 1696*112^n+1 809 1M* 1474*117^n+1 652 500K 48*118^n+1 980 740K* 34*122^n+1 738 1M 40*128^n+1 917 1.2857M* 8*140^n+1 435 1M 2361*148^n+1 1810 1M* 4*155^n+1 1738 1.3M pepi37 4*174^n+1 765 850K* 8*182^n+1 269 1M* 10*185^n+1 1350 1M* 40*200^n+1 624 1M* 4*204^n+1 1176 600K* 1356*217^n+1 1316 500K* 17*218^n+1 732 500K* 18*227^n+1 242 1M* 4*230^n+1 793 1M 27*252^n+1 1855 500K* 831*256^n+1 1999 1M 40*257^n+1 1355 600K 64*259^n+1 391 1M* 8*263^n+1 298 1M 41*264^n+1 1098 600K* 61*294^n+1 1440 600K* 60*304^n+1 228 1M* 44*317^n+1 797 500K 89*318^n+1 1009 500K 97*320^n+1 740 500K* 27*328^n+1 758 1M 4*335^n+1 1287 1M* 199*340^n+1 1195 600K* 8*353^n+1 613 600K* 108*373^n+1 547 400K* BOINC 156*379^n+1 2052 400K* BOINC 20*401^n+1 456 1M* 61*402^n+1 1665 500K* 10*417^n+1 1569 400K* BOINC 8*426^n+1 802 400K* BOINC 8*428^n+1 397 500K* 15321*430^n+1 483 500K 87*450^n+1 1275 500K* 2*461^n+1 1184 400K* BOINC 4*467^n+1 665 750K* 97*468^n+1 972 889K* wombatman 32*470^n+1 1401 400K* BOINC 28*476^n+1 1262 400K* BOINC 12*480^n+1 1175 500K* 69*492^n+1 652 400K* BOINC 8*497^n+1 738 500K 5*512^n+1 869 1M* 122*516^n+1 1154 400K* 369*520^n+1 1487 700K* BOINC 104*534^n+1 802 400K* 94*550^n+1 658 500K* 16*574^n+1 1008 400K* 6*579^n+1 1366 400K* 32*582^n+1 1118 400K* 136*596^n+1 1077 400K* 70*605^n+1 1614 400K* 32*638^n+1 497 500K* 64*649^n+1 825 400K* 607*676^n+1 1075 400K* 106*678^n+1 1143 500K* 116*686^n+1 1332 400K* 39*702^n+1 1129 400K* 40*707^n+1 783 400K* 13*720^n+1 1521 400K* 9*724^n+1 1573 400K* 84*730^n+1 1192 400K* 12*736^n+1 1431 400K* 13*740^n+1 1350 1M 8*758^n+1 501 500K* 163*778^n+1 1247 400K* 370*781^n+1 2853 400K* 151*784^n+1 1697 400K* 8*785^n+1 410 500K* 96*789^n+1 1386 500K 33*798^n+1 878 400K* 4*803^n+1 889 500K* 140*806^n+1 1171 400K* 153*816^n+1 793 400K* 80*821^n+1 997 500K* 8*828^n+1 529 500K* 89*834^n+1 1214 400K* 2*836^n+1 1851 400K* 252*850^n+1 1003 400K* 106*853^n+1 987 1M 74*864^n+1 2012 500K* 8*866^n+1 440 400K* matzetoni 4*875^n+1 1231 1M* 66*883^n+1 1390 500K 2*914^n+1 2107 400K* 2*917^n+1 549 400K* 8*930^n+1 1144 400K* 10*935^n+1 1795 400K* 8*953^n+1 795 400K* 11*968^n+1 1470 400K* 25*980^n+1 1040 400K* 8*983^n+1 853 400K* 12*998^n+1 1066 400K* 2*1004^n+1 809 400K* 144*1009^n+1 1607 400K* Code:
test reservation/ form weight limit comments 1597*6^n1 272 5.3M masser 4421*10^n1 571 2.34M Cruelty 3656*22^n1 807 5M 404*23^n1 580 2M* 706*27^n1 770 5M 55758*31^n1 2309 3M 424*93^n1 1386 779K* 29*94^n1 1046 1M* 924*103^n1 1317 575K* 84*109^n1 1732 800K* BOINC 24*123^n1 2758 555K* 926*133^n1 1570 550K* 116*160^n1 769 600K* 254*163^n1 995 600K* 22*173^n1 1098 800K* BOINC 168*181^n1 1739 600K* 294*213^n1 2285 500K* 11*214^n1 913 1M* 32*221^n1 1317 600K* 10*233^n1 1843 600K* 6*234^n1 1310 600K* 1854*253^n1 1666 1M* 4*275^n1 1472 600K* 122*318^n1 309 1M 8*321^n1 817 500K* 50*326^n1 1642 600K* 8*328^n1 774 1M* 18*332^n1 2502 600K* 16*333^n1 1389 1M* 14*334^n1 1318 600K* 22*347^n1 402 500K* 71*354^n1 1243 600K* 1747*366^n1 1424 1.3M PuzzlePeter 36*368^n1 812 600K* 18*373^n1 452 500K* 7*392^n1 846 500K* 7*398^n1 761 500K* 38*401^n1 966 600K* 32*402^n1 1126 600K* 6*412^n1 889 600K* 55*416^n1 1191 600K* 64*425^n1 948 400K* 11*458^n1 343 600K* 422*469^n1 1275 400K* 137*470^n1 1127 400K* 92*493^n1 1212 400K* 57*496^n1 2063 400K* 94*504^n1 1197 400K* 68*505^n1 1919 400K* 87*516^n1 1274 400K* 74*533^n1 690 400K* 7*548^n1 1320 400K* 6*549^n1 610 400K* 10*551^n1 1123 400K* 28*563^n1 1210 400K* 6*573^n1 1077 400K* 2*581^n1 1856 400K* 52*582^n1 1243 400K* 234*610^n1 519 400K* 10*611^n1 1494 400K* 12*615^n1 945 400K* 6*619^n1 1371 400K* 78*622^n1 900 400K* 9*636^n1 1758 1M* 4*650^n1 1122 400K* 7*662^n1 638 500K* 8*665^n1 972 400K* 11*668^n1 918 400K* 174*679^n1 1232 400K* 39*684^n1 1593 400K* 9*688^n1 641 400K* 26*695^n1 1351 400K* 32*702^n1 2216 400K* 47*712^n1 474 726K* MisterBitcoin 8*727^n1 1151 400K* 170*730^n1 1976 400K* 34*731^n1 1463 400K* 560*736^n1 1147 400K* 14*743^n1 770 400K* 32*761^n1 1416 400K* 38*773^n1 1427 400K* 14*782^n1 925 400K* 104*783^n1 1263 400K* 116*784^n1 1300 400K* 48*790^n1 1343 400K* 8*800^n1 1652 1M* 4*812^n1 1052 400K* 122*813^n1 1164 400K* 8*815^n1 1988 400K* 104*833^n1 827 400K* 8*836^n1 1446 400K* 221*850^n1 1414 400K* 114*864^n1 946 400K* 8*867^n1 475 400K* 24*879^n1 2118 400K* 194*883^n1 850 500K 64*888^n1 891 600K* 22*905^n1 748 400K* 8*958^n1 441 500K* 242*967^n1 1509 500K* 4*968^n1 938 500K 20*995^n1 1395 500K* 2*1019^n1 1424 400K* 29*1024^n1 928 1M* 8*1025^n1 1069 1.075M* 26*1029^n1 1454 1M* Last fiddled with by gd_barnes on 20210126 at 12:28 Reason: update status 
20100112, 20:45  #2  
May 2007
Kansas; USA
10284_{10} Posts 
Quote:
Great idea, Mark, about starting this thread. Yeah, I'd be screaming about updating the pages any more than I have to right now but I have about as good of an idea: Just have threads like this and have Max or me keep the 1st post in them updated. I'm just the idea and detail guy but admittedly am not a particularly good coordinator of things. So if anyone wants to take the lead in coordinating huge projectwide sieving efforts for bases like this, be my guest. I haven't given the project a whole lot of direction and that's largely because it is so huge and allencompassing. I'll take this one step further: Neither I nor CRUS own all of this stuff. It's so huge so as to be almost unmanageable at times. I'd be perfectly happy if someone wanted to take a base or two (or several) and make a separate project out of it. I'll be glad to offer tips on getting a project or subforum started. KEP even has mentioned a couple of times taking some of the project to BOINC. Although I'm not a BOINC fan, that'd be fine with me on a few of the bases with huge #'s of k's or bases where the search depth is already so high that few of our contributors are interested in them. Sierp base 4 at n=1M is a good example there. Riesel base 6 will likely get to that point also as we near n=1M. It's stalled at n=~520K right now. Edit: I made a few corrections and added several more bases to the 1st post here. Mark, 2 of them are reserved by you! :) Gary Last fiddled with by gd_barnes on 20100124 at 04:28 Reason: edit 

20100112, 21:29  #3 
"Mark"
Apr 2003
Between here and the
2^{4}×3^{2}×43 Posts 
I thought that I released those bases. Maybe I wasn't clear in the reservations thread. I had taken those bases to 25K and released them. I might get back to them, but not for a month or more. Base 928 will take a while to get to 25K and I can't do that until Riesel base 58 is to 50K, which should complete in about three weeks.

20100112, 22:13  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
http://www.noprimeleftbehind.net/cru...ereserves.htm has this as reserved to 25K by rogue. Is that correct?

20100112, 22:26  #5  
"Mark"
Apr 2003
Between here and the
6192_{10} Posts 
Quote:


20100113, 06:36  #6 
May 2007
Kansas; USA
2^{2}×3×857 Posts 
Mark,
I see what happened now. In this post, you stated that "these are all searched to n=25K". I took that to mean that you had tested all of the bases below that statement (i.e. the ones with primes) to n=25K. I did not take it to mean that you had tested all of the above bases (in the blue box) to n=25K. In the context stated, I can see now that my interpretation was incorrect. I can see why I did too. That's a lot of bases without any primes for n=10K25K! I'll update the pages for that confusion in just a little while. One question: Like I said, that's a lot of bases with no primes for n=10K25K and at least one that should have been for n=2.5K25K. Are you absolutely positive that all listed bases in that post were tested to n=25K? The best example of one that I'm concerned about: Sierp base 811. Did you test this for n=2.5K25K? It's testing limit was only n=2.5K when you reserved it and it's very unusual that no primes were found for 5 k's over such a low and wide nrange. Sierp base 961 is another example. Bases where b==(1 mod 30) are generally highweight bases yet there were no primes for n=10K25K for 9 k's on S961, which makes no primes for 14 k's for n=10K25K combined on highweight bases. I'm not saying these are wrong; just very unusual. Can you do a close check of your primes file and make sure all were listed? Can you please provide results files for any or all of these and for any future testing for n>2500? Personally I get quite paranoid just taking people's word for it that they've searched a base to a certain depth without supporting results, especially at the very high nranges. With this few primes on this many bases, with no results files, I'm inclined to start a doublecheck effort for them. Here is what is left that I now show as reserved by you: Riesel and Sierp bases 322, 328, 422, 516, 520, 803, and 928. Can you let me know if that is correct? Thanks, Gary Last fiddled with by gd_barnes on 20100113 at 07:07 
20100113, 13:46  #7 
"Mark"
Apr 2003
Between here and the
2^{4}×3^{2}×43 Posts 
Those are the k I have reserved.
I will go back and see if I forgot to report some primes on those other bases. 
20100113, 14:31  #8  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Just to add some real numbers to Gary's speculation/worrying:
Quote:
Quote:
Looks like the math is in Gary's favor. It does seem quite odd that those don't have any primes. Last fiddled with by MiniGeek on 20100113 at 14:35 Reason: bolded the important parts 

20100113, 23:24  #9 
May 2007
Kansas; USA
2^{2}·3·857 Posts 
Thanks Kenneth. It was correct on the pages and incorrect in the 1st post. I've now corrected it. I've now reviewed every base on the pages and have confirmed that the 1st post here is synced up with them.
One note: I just recently reserved Sierp bases 122 and 129 and found that they had one k remaining at n=2500. I think I'll make it a point to only list bases in the 1st post here that have already been searched to n=25K. If I reach n=25K on those bases without a prime, I'll add them to the 1st post. Last fiddled with by gd_barnes on 20100113 at 23:32 
20100113, 23:36  #10  
May 2007
Kansas; USA
282C_{16} Posts 
Quote:
Thanks for the analogy Tim. Actually there should be even more expected primes with a less chance of no prime. That's because the percentage reduction is not linear. Although it can vary quite a bit based on the ratio between the high and low n, instead of taking the average nvalue, it's likely better here to take an nvalue around 3540% of the nrange. Regardless, even without that adjustment, wow! 10.418%*12.942% = 1.35%. So there's a collective only 1.35% chance that bases 811 and 961 don't have a prime. Interesting. Last fiddled with by gd_barnes on 20100114 at 05:04 

20100114, 00:17  #11  
"Mark"
Apr 2003
Between here and the
1830_{16} Posts 
Quote:


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