Conjectures with one k remaining

rogue · 2010-01-12, 19:53

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*

Riesel Conjectures:

Code:

                     test    reservation/
     form     weight limit   comments
   1597*6^n-1   272  5.3M    masser
  4421*10^n-1   571  2.34M   Cruelty
  3656*22^n-1   807  5M
   404*23^n-1   580  2M*
   706*27^n-1   770  5M
 55758*31^n-1  2309  3M
   424*93^n-1  1386  779K*
    29*94^n-1  1046  1M*
  924*103^n-1  1317  575K*
   84*109^n-1  1732  800K*   BOINC
   24*123^n-1  2758  555K*
  926*133^n-1  1570  550K*
  116*160^n-1   769  600K*
  254*163^n-1   995  600K*
   22*173^n-1  1098  800K*   BOINC
  168*181^n-1  1739  600K*
  294*213^n-1  2285  500K*
   11*214^n-1   913  1M*
   32*221^n-1  1317  600K*
   10*233^n-1  1843  600K*
    6*234^n-1  1310  600K*
 1854*253^n-1  1666  1M*
    4*275^n-1  1472  600K*
  122*318^n-1   309  1M
    8*321^n-1   817  500K*
   50*326^n-1  1642  600K*
    8*328^n-1   774  1M*
   18*332^n-1  2502  600K*
   16*333^n-1  1389  1M*
   14*334^n-1  1318  600K*
   22*347^n-1   402  500K*
   71*354^n-1  1243  600K*
 1747*366^n-1  1424  1.3M    Puzzle-Peter
   36*368^n-1   812  600K*
   18*373^n-1   452  500K*
    7*392^n-1   846  500K*
    7*398^n-1   761  500K*
   38*401^n-1   966  600K*
   32*402^n-1  1126  600K*
    6*412^n-1   889  600K*
   55*416^n-1  1191  600K*
   64*425^n-1   948  400K*
   11*458^n-1   343  600K*
  422*469^n-1  1275  400K*
  137*470^n-1  1127  400K*
   92*493^n-1  1212  400K*
   57*496^n-1  2063  400K*
   94*504^n-1  1197  400K*
   68*505^n-1  1919  400K*
   87*516^n-1  1274  400K*
   74*533^n-1   690  400K*
    7*548^n-1  1320  400K*
    6*549^n-1   610  400K*
   10*551^n-1  1123  400K*
   28*563^n-1  1210  400K*
    6*573^n-1  1077  400K*
    2*581^n-1  1856  400K*
   52*582^n-1  1243  400K*
  234*610^n-1   519  400K*
   10*611^n-1  1494  400K*
   12*615^n-1   945  400K*
    6*619^n-1  1371  400K*
   78*622^n-1   900  400K*
    9*636^n-1  1758  1M*
    4*650^n-1  1122  400K*
    7*662^n-1   638  500K*
    8*665^n-1   972  400K*
   11*668^n-1   918  400K*
  174*679^n-1  1232  400K*
   39*684^n-1  1593  400K*
    9*688^n-1   641  400K*
   26*695^n-1  1351  400K*
   32*702^n-1  2216  400K*
   47*712^n-1   474  726K*   MisterBitcoin
    8*727^n-1  1151  400K*
  170*730^n-1  1976  400K*
   34*731^n-1  1463  400K*
  560*736^n-1  1147  400K*
   14*743^n-1   770  400K*
   32*761^n-1  1416  400K*
   38*773^n-1  1427  400K*
   14*782^n-1   925  400K*
  104*783^n-1  1263  400K*
  116*784^n-1  1300  400K*
   48*790^n-1  1343  400K*
    8*800^n-1  1652  1M*
    4*812^n-1  1052  400K*
  122*813^n-1  1164  400K*
    8*815^n-1  1988  400K*
  104*833^n-1   827  400K*
    8*836^n-1  1446  400K*
  221*850^n-1  1414  400K*
  114*864^n-1   946  400K*
    8*867^n-1   475  400K*
   24*879^n-1  2118  400K*
  194*883^n-1   850  500K
   64*888^n-1   891  600K*
   22*905^n-1   748  400K*
    8*958^n-1   441  500K*
  242*967^n-1  1509  500K*
    4*968^n-1   938  500K
   20*995^n-1  1395  500K*
   2*1019^n-1  1424  400K*
  29*1024^n-1   928  1M*
   8*1025^n-1  1069  1.075M*
  26*1029^n-1  1454  1M*

Gary, I wonder if it would be useful to have webpages listing "tested conjectures by fewest k remaining", "tested conjectures by lowest n", and "untested conjectures by fewest k". I can hear you screaming now. :-)

gd_barnes · 2010-01-12, 20:45

Quote:

Originally Posted by rogue

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 a someone to get lucky.

Sierpinski Conjectures:
(etc.)

Gary, I wonder if it would be useful to have webpages listing "tested conjectures by fewest k remaining", "tested conjectures by lowest n", and "untested conjectures by fewest k". I can hear you screaming now. :-)

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 project-wide 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 all-encompassing.

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 sub-forum 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

rogue · 2010-01-12, 21:29

Quote:

Originally Posted by gd_barnes

Edit: I made a few corrections and added several more bases to the 1st post here. Mark, 2 of them are reserved by you! :-)

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.

Mini-Geek · 2010-01-12, 22:13

Quote:

Originally Posted by rogue

Code:

 370*781^n+1 (n< 10K)

http://www.noprimeleftbehind.net/cru...e-reserves.htm has this as reserved to 25K by rogue. Is that correct?

rogue · 2010-01-12, 22:26

Quote:

Originally Posted by Mini-Geek

http://www.noprimeleftbehind.net/cru...e-reserves.htm has this as reserved to 25K by rogue. Is that correct?

I completed it to 25K. Gary must have missed it.

gd_barnes · 2010-01-13, 06:36

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=10K-25K!

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=10K-25K and at least one that should have been for n=2.5K-25K. 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=2.5K-25K? 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 n-range. Sierp base 961 is another example. Bases where b==(1 mod 30) are generally high-weight bases yet there were no primes for n=10K-25K for 9 k's on S961, which makes no primes for 14 k's for n=10K-25K combined on high-weight 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 n-ranges. With this few primes on this many bases, with no results files, I'm inclined to start a double-check 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

rogue · 2010-01-13, 13:46

Those are the k I have reserved.

I will go back and see if I forgot to report some primes on those other bases.

Mini-Geek · 2010-01-13, 14:31

Just to add some real numbers to Gary's speculation/worrying:

Quote:

Originally Posted by gd_barnes

The best example of one that I'm concerned about: Sierp base 811. Did you test this for n=2.5K-25K? 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 n-range.

Sieving this to 1G leaves 5643 candidates. Assuming an average n of 13750 (half way between 2.5K and 25K), we should expect 2.261 primes. That's an 89.582% chance of at least 1 prime, or a 10.418% chance of no primes.

Quote:

Originally Posted by gd_barnes

Sierp base 961 is another example. Bases where b==(1 mod 30) are generally high-weight bases yet there were no primes for n=10K-25K for 9 k's on S961, which makes no primes for 14 k's for n=10K-25K combined on high-weight bases. I'm not saying these are wrong; just very unusual.

Sieving this to 1M leaves 9987 candidates. Assuming an average n of 17500 (half way between 10K and 25K), we should expect 2.044 primes. That's an 87.058% chance of at least 1 prime, or a 12.942% chance of no primes.

Looks like the math is in Gary's favor. It does seem quite odd that those don't have any primes.

gd_barnes · 2010-01-13, 23:24

Quote:

Originally Posted by KEP

k=27 for sierp base 252 is tested to n=100K

Regards

KEP

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.

gd_barnes · 2010-01-13, 23:36

Quote:

Originally Posted by Mini-Geek

Just to add some real numbers to Gary's speculation/worrying:

Sieving this to 1G leaves 5643 candidates. Assuming an average n of 13750 (half way between 2.5K and 25K), we should expect 2.261 primes. That's an 89.582% chance of at least 1 prime, or a 10.418% chance of no primes.

Sieving this to 1M leaves 9987 candidates. Assuming an average n of 17500 (half way between 10K and 25K), we should expect 2.044 primes. That's an 87.058% chance of at least 1 prime, or a 12.942% chance of no primes.

Looks like the math is in Gary's favor. It does seem quite odd that those don't have any primes.

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 n-value, it's likely better here to take an n-value around 35-40% of the n-range.

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.

rogue · 2010-01-14, 00:17

Quote:

Originally Posted by gd_barnes

Thanks for the analogy Tim. Actually there should be even more primes with a less change 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 n-value, it's likely better here to take an n-value around 35-40% of the n-range.

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.

Although it appears to me that I did test the entire range, I found no primes in it for those bases. So far I have retested 811 to about 9200 and haven't found a prime.

2010-01-13, 06:36	#6
gd_barnes May 2007 Kansas; USA 2²×3×857 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=10K-25K! 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=10K-25K and at least one that should have been for n=2.5K-25K. 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=2.5K-25K? 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 n-range. Sierp base 961 is another example. Bases where b==(1 mod 30) are generally high-weight bases yet there were no primes for n=10K-25K for 9 k's on S961, which makes no primes for 14 k's for n=10K-25K combined on high-weight 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 n-ranges. With this few primes on this many bases, with no results files, I'm inclined to start a double-check 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 2010-01-13 at 07:07

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2010-01-13, 13:46	#7
rogue "Mark" Apr 2003 Between here and the 2⁴×3²×43 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.