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rogue 2010-01-12 19:53

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 2M
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*
10438*70^n+1 1054 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 800K*
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 1.5M pepi37
4*174^n+1 765 1M*
8*182^n+1 269 1M*
10*185^n+1 1350 1M*
40*200^n+1 624 1M*
4*204^n+1 1176 1M*
1356*217^n+1 1316 500K* BOINC
17*218^n+1 732 600K*
18*227^n+1 242 1M*
4*230^n+1 793 1M*
27*252^n+1 1855 500K* BOINC
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 1M*
61*294^n+1 1440 1M*
60*304^n+1 228 1M*
44*317^n+1 797 600K*
89*318^n+1 1009 600K*
97*320^n+1 740 500K*
27*328^n+1 758 1M*
4*335^n+1 1287 1M*
199*340^n+1 1195 1M
8*353^n+1 613 700K*
108*373^n+1 547 700K*
156*379^n+1 2052 1M*
20*401^n+1 456 1M*
61*402^n+1 1665 500K*
10*417^n+1 1569 700K*
8*426^n+1 802 600K*
8*428^n+1 397 600K*
15321*430^n+1 483 600K*
87*450^n+1 1275 600K*
2*461^n+1 1184 600K*
4*467^n+1 665 885K* pepi37
97*468^n+1 972 1M wombatman
28*476^n+1 1262 600K*
12*480^n+1 1175 600K*
69*492^n+1 652 600K*
8*497^n+1 738 600K*
5*512^n+1 869 1M*
122*516^n+1 1154 600K*
369*520^n+1 1487 1M
104*534^n+1 802 600K*
94*550^n+1 658 600K*
16*574^n+1 1008 600K*
6*579^n+1 1366 600K*
32*582^n+1 1118 600K*
136*596^n+1 1077 600K*
70*605^n+1 1614 600K*
32*638^n+1 497 600K*
64*649^n+1 825 600K*
106*678^n+1 1143 500K*
116*686^n+1 1332 600K*
39*702^n+1 1129 600K*
40*707^n+1 783 600K*
13*720^n+1 1521 500K*
9*724^n+1 1573 500K*
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 500K*
4*875^n+1 1231 1M*
66*883^n+1 1390 500K*
2*914^n+1 2107 400K*
2*917^n+1 549 500K*
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 600K*
144*1009^n+1 1607 400K*
[/code]Riesel Conjectures:
[code]
test reservation/
form weight limit comments
1597*6^n-1 272 5.6M masser
4421*10^n-1 571 2M
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 600K*
84*109^n-1 1732 1M
24*123^n-1 2758 600K*
926*133^n-1 1570 600K*
116*160^n-1 769 600K*
254*163^n-1 995 600K*
22*173^n-1 1098 1M
168*181^n-1 1739 600K*
294*213^n-1 2285 600K*
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 600K*
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 600K*
71*354^n-1 1243 600K*
1747*366^n-1 1424 2M
36*368^n-1 812 600K*
18*373^n-1 452 600K*
7*392^n-1 846 600K*
7*398^n-1 761 600K*
38*401^n-1 966 600K*
32*402^n-1 1126 600K*
6*412^n-1 889 600K*
55*416^n-1 1191 600K*
11*458^n-1 343 700K*
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 600K*
7*548^n-1 1320 400K*
6*549^n-1 610 600K*
10*551^n-1 1123 400K*
28*563^n-1 1210 400K*
6*573^n-1 1077 400K*
2*581^n-1 1856 400K* rogue
52*582^n-1 1243 400K* rogue
234*610^n-1 519 500K*
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*
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 1M
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 500K*
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 600K*
29*1024^n-1 928 1M*
8*1025^n-1 1069 1.075M*
26*1029^n-1 1454 1M*
[/code]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=rogue;201642]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. :-)[/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 :smile: 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=gd_barnes;201657]Edit: I made a few corrections and added several more bases to the 1st post here. Mark, 2 of them are reserved by you! :-)[/QUOTE]

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=rogue;201642][code] 370*781^n+1 (n< 10K)[/code][/quote]
[url]http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm[/url] has this as reserved to 25K by rogue. Is that correct?

rogue 2010-01-12 22:26

[QUOTE=Mini-Geek;201670][url]http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm[/url] has this as reserved to 25K by rogue. Is that correct?[/QUOTE]

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

gd_barnes 2010-01-13 06:36

Mark,

I see what happened now. In [URL="http://www.mersenneforum.org/showpost.php?p=201400&postcount=870"]this post[/URL], you stated that "these are all searched to n=25K". I took that to mean that you had tested all of the bases [I]below[/I] 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 [I]above[/I] 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=gd_barnes;201715]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.[/quote]
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 [B]10.418% chance of no primes[/B].
[quote=gd_barnes;201715]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.[/quote]
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 [B]12.942% chance of no primes[/B].

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=KEP;201751]k=27 for sierp base 252 is tested to n=100K :smile:

Regards

KEP[/quote]

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=Mini-Geek;201760]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 [B]10.418% chance of no primes[/B].

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 [B]12.942% chance of no primes[/B].

Looks like the math is in Gary's favor. It does seem quite odd that those don't have any primes.[/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 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=gd_barnes;201829]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.[/QUOTE]

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.


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