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 Register FAQ Search Today's Posts Mark Forums Read  2016-12-18, 18:58 #34 sweety439   Nov 2016 1000101101112 Posts base 11, d=6: Tested to 470000, I still found no such k.   2016-12-18, 19:12 #35 Batalov   "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22×2,281 Posts We need updates at 15 minute intervals. You are getting sloppy -- too few updates!   2016-12-18, 19:12 #36 sweety439   Nov 2016 23×97 Posts Due to the CRUS, if we only consider the k's with cover set (i.e. not with full or partial algebra factors), then the conjectured k's for some cases should be larger: base 4, d=1: 5 (11) --> 120 (1320) base 4, d=3: 8 (20) --> 39938 (21300002) base 9, d=1: 1 (1) --> 5 (5) base 9, d=8: 3 (3) --> 73 (81) base 12, d=1: 40 (34) --> 117 (99) base 12, d=E: 24 (20) --> 375 (273) All these conjectures are proven except base 4 d=3, which is the same as the Riesel base 4 conjecture. Note: In the base 12 d=1 case, k=40 (34) and 105 (89) are proven composite by partial algebra factors. Last fiddled with by sweety439 on 2016-12-18 at 19:15   2016-12-19, 05:06 #37 gd_barnes   May 2007 Kansas; USA 23×3×52×17 Posts Nice work Sweety. This is what we have been looking for. That is a reasonable amount of actual calculations or searching on your part. You might consider making a new single post similar to the first post in this thread with all of the new information that has been shown in this thread. Be sure and include my work as well as the base 11 conjectures that you have found as well as how many k's remain for each one. If you were to create a web page that you could periodically update with efforts done by everyone you might get some more people interested in searching these. In the mean time, I have an update of my own in the next post. Last fiddled with by gd_barnes on 2016-12-19 at 05:41   2016-12-19, 05:32 #38 gd_barnes   May 2007 Kansas; USA 27D816 Posts base 6 d=1 I did some doublecheck work on base 6 d=1 to n=15K and then extended it to n=25K. There are 24 k's remaining at n=25K. One outright error and three inconsistencies were found on the Composite Sequences page as follows: Inconsistencies: 1. Before the table he states the following: "There are 29 candidate seed values less than 26789 checked to 15000 digits." Within the table he shows that the remaining k's are only "composite to n=13000". As it turns out, there are no primes for the n=12K-15K range so it's not clear weather they were searched to n=13K or 15K. 2. For k=98, he shows a prime at n=3041. K=98 actually has a prime at n=3. As it turns out it is k=21211 that has a prime at n=3038. This is the same prime as k=98 n=3041. But it is shown incorrectly and is misleading. (Note that the same prime for k=98 n=3 would be k=21211 n=0 but n must be > 0 hence it is not allowed so k=21211 must continue to be searched.) 3. For k=575, he shows a prime at n=6476. K=575 actually has a prime at n=2. The same situation exists as in #2. As it turns out k=20707 has a prime at n=6474. This is the same prime as k=575 n=6476. But once again it is shown incorrectly and is misleading. Outright error (bad bad!): k=16982 is shown with a prime somewhere in the n=9K-13K range leaving 29 k's remaining at n=15K. This is incorrect. There is no prime for k=16982 all the way to n=25K. I even doublechecked myself to n=15K resulting in an actual triple check. Therefore there are actually 30 k's remaining at n=15K. Primes for n>5000: Code:  k n 848 7056 1666 10461 4606 11921 5292 11657 6804 5807 6966 6820 7575 8976 8127 18749 10907 24822 11165 5103 12285 5009 15359 10630 17675 5337 20616 20652 20707 6474 21147 10851 22058 5566 22163 5130 22940 15238 23016 15043 23786 7031 25494 21425 24 k's remaining at n=25K: Code:  525 1247 1898 7406 9954 10137 10788 11012 11585 15352 15960 16682 16982 17243 17759 18592 20770 21868 22232 23758 24683 25277 25788 26495 It is my suggestion that the Composite Sequences page should be double checked before accepting its results. I will be done with b=12 d=5 to n=25K tomorrow. Last fiddled with by gd_barnes on 2016-12-19 at 05:41   2016-12-20, 03:40 #39 gd_barnes   May 2007 Kansas; USA 23·3·52·17 Posts base 12 d=5 I continued my work on base 12 d=5. All k's have now been searched to n=25K. 11 primes were found for n=10K-25K. There are 31 k's remaining. Primes for n=10K-25K: Code:  k n 9313 20776 12272 10721 13811 13280 19427 12114 21286 18358 25784 10216 28826 14710 29874 22297 30308 13620 30862 17489 31283 12044 31 k's remaining at n=25K: Code: 4446 4927 6123 6591 6656 7761 10543 12043 12498 13572 15137 15691 15756 18504 19609 20532 21086 22417 23946 24492 24822 25251 26187 26278 27001 27166 27383 28561 29822 31499 32661 I am done working on this one. Last fiddled with by gd_barnes on 2016-12-20 at 03:41   2016-12-20, 06:10 #40 gd_barnes   May 2007 Kansas; USA 23·3·52·17 Posts The conjecture for base 11 d=6 is k=1669093. The covering set is [7 13 19 37 61]. This is the largest conjecture found for d 2016-12-20, 06:37 #41 gd_barnes   May 2007 Kansas; USA 27D816 Posts I did some quick searching on most of the base 11 conjectures to n=5K in order to see where they are at. Here is what I found: digit / conjectured k [covering set] / # of k's remaining / (list of k's remaining) d=1: CK=3 [2, 3]; proven d=2: CK=2627 [3, 7, 19, 37]; 14 k's remain; (k=501, 513, 555, 653, 857, 1067, 1183, 1297, 1337, 1367, 1563, 1781, 2299, 2439) d=3: CK=1520 [2, 7, 19, 37]; 22 k's remain; (k=17, 178, 188, 379, 395, 511, 551, 589, 625, 682, 770, 820, 826, 829, 929, 988, 1073, 1135, 1178, 1205, 1366, 1436) d=4: CK=973 [3, 7, 19, 37]; 6 k's remain; (k=25, 61, 333, 745, 837, 865) d=5: CK=2 [2,3]; proven d=6: CK=1669093 [7, 13, 19, 37, 61]; (no searching done) d=7: CK=3 [2, 3]; proven d=8: CK=4625 [3, 7, 19, 37]; 25 k's remain; (k=57, 131, 191, 533, 609, 743, 747, 893, 1167, 1253, 1387, 1739, 1769, 1961, 2147, 2231, 2441, 2795, 2931, 2963, 3903, 4047, 4053, 4409, 4523) d=9: CK=716 [2, 7, 19, 37]; 5 k's remain; (k=70, 227, 337, 436, 535) d=A: CK=861 [3, 7, 19, 37]; proven Last fiddled with by gd_barnes on 2016-12-20 at 06:38   2016-12-20, 17:54   #42
sweety439

Nov 2016

23×97 Posts Quote:
 Originally Posted by sweety439 Due to the CRUS, if we only consider the k's with cover set (i.e. not with full or partial algebra factors), then the conjectured k's for some cases should be larger: base 4, d=1: 5 (11) --> 120 (1320) base 4, d=3: 8 (20) --> 39938 (21300002) base 9, d=1: 1 (1) --> 5 (5) base 9, d=8: 3 (3) --> 73 (81) base 12, d=1: 40 (34) --> 117 (99) base 12, d=E: 24 (20) --> 375 (273) All these conjectures are proven except base 4 d=3, which is the same as the Riesel base 4 conjecture. Also see http://mersenneforum.org/showthread.php?t=21839&page=2 (my research for the strong (extended) Sierpinski/Riesel problem) Note: In the base 12 d=1 case, k=40 (34) and 105 (89) are proven composite by partial algebra factors.
The cover set of them are:

base 4 d=1 k=120: {3, 5, 7, 13}
base 4 d=3 k=39938: {5, 7, 13, 19, 73, 109}
base 9 d=1 k=5: {2, 5}
base 9 d=8 k=73: {5, 7, 13, 73}
base 12 d=1 k=117: {5, 13, 29}
base 12 d=E k=375: {5, 13, 29}

These are the primes of these conjectures (except base 4 d=3)

Also see http://mersenneforum.org/showthread.php?t=21839&page=2 (my research for the strong (extended) Sierpinski/Riesel problem)
Attached Files base-4-digit-1.txt (796 Bytes, 73 views) base-9-digit-1.txt (32 Bytes, 68 views) base-9-digit-8.txt (235 Bytes, 52 views) base-12-digit-1.txt (730 Bytes, 71 views) base-12-digit-E.txt (2.3 KB, 52 views)

Last fiddled with by sweety439 on 2016-12-20 at 17:58   2017-01-04, 16:39   #43
sweety439

Nov 2016

1000101101112 Posts Quote:
 Originally Posted by gd_barnes I did some quick searching on most of the base 11 conjectures to n=5K in order to see where they are at. Here is what I found: digit / conjectured k [covering set] / # of k's remaining / (list of k's remaining) d=1: CK=3 [2, 3]; proven d=2: CK=2627 [3, 7, 19, 37]; 14 k's remain; (k=501, 513, 555, 653, 857, 1067, 1183, 1297, 1337, 1367, 1563, 1781, 2299, 2439) d=3: CK=1520 [2, 7, 19, 37]; 22 k's remain; (k=17, 178, 188, 379, 395, 511, 551, 589, 625, 682, 770, 820, 826, 829, 929, 988, 1073, 1135, 1178, 1205, 1366, 1436) d=4: CK=973 [3, 7, 19, 37]; 6 k's remain; (k=25, 61, 333, 745, 837, 865) d=5: CK=2 [2,3]; proven d=6: CK=1669093 [7, 13, 19, 37, 61]; (no searching done) d=7: CK=3 [2, 3]; proven d=8: CK=4625 [3, 7, 19, 37]; 25 k's remain; (k=57, 131, 191, 533, 609, 743, 747, 893, 1167, 1253, 1387, 1739, 1769, 1961, 2147, 2231, 2441, 2795, 2931, 2963, 3903, 4047, 4053, 4409, 4523) d=9: CK=716 [2, 7, 19, 37]; 5 k's remain; (k=70, 227, 337, 436, 535) d=A: CK=861 [3, 7, 19, 37]; proven
hi, Gary.

Did you search the base 11 conjectures to n=25K?

Of course, there are k's included in the conjectures but excluded from testing. e.g. base 11 d=3 k=190, since 190=17*11+3 and 190 is not prime. Thus, k=190 will have the same prime as k=17.

Last fiddled with by sweety439 on 2017-01-04 at 16:42   2017-01-05, 08:06   #44
gd_barnes

May 2007
Kansas; USA

23·3·52·17 Posts Quote:
 Originally Posted by sweety439 hi, Gary. Did you search the base 11 conjectures to n=25K? Of course, there are k's included in the conjectures but excluded from testing. e.g. base 11 d=3 k=190, since 190=17*11+3 and 190 is not prime. Thus, k=190 will have the same prime as k=17.
I am aware of which k's are included but don't need to be tested.

I have searched and doublechecked nearly all bases <= 12 for all digits to n=25K beginning from scratch. Many errors have been found on the Composite Sequences pages so I concluded that those are not a good starting point. They should be mostly ignored. The only bases/digits that I have NOT finished yet are:

base 5, d=2; currently at n=20K; testing ongoing to n=25K
base 5, d=3; testing not started
base 8, d=3; currently at n=10K; testing ongoing to n=25K
base 11, d=6; currently at n=10K; testing to n=25K will begin after b5d2 and b8d3 are complete.

All other base/digit combos are at n>=25K. I will post all results when everything except b5d3 is finished. B5d3 will take a quite a while because it is one of the few large-conjectured base/digit combos that cannot be normally sieved at all.   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post a1call Miscellaneous Math 179 2015-11-12 14:59 sinide Factoring 12 2010-11-09 01:05 aaa120 Factoring 19 2010-09-04 09:16 storm5510 Other Mathematical Topics 14 2010-08-31 01:16 Unregistered Math 11 2004-11-30 22:53

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