20161218, 18:58  #34 
Nov 2016
100010110111_{2} Posts 
base 11, d=6: Tested to 470000, I still found no such k.

20161218, 19:12  #35 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
We need updates at 15 minute intervals. You are getting sloppy  too few updates!

20161218, 19:12  #36 
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 20161218 at 19:15 
20161219, 05:06  #37 
May 2007
Kansas; USA
2^{3}×3×5^{2}×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 20161219 at 05:41 
20161219, 05:32  #38 
May 2007
Kansas; USA
27D8_{16} 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=12K15K 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=9K13K 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 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 I will be done with b=12 d=5 to n=25K tomorrow. Last fiddled with by gd_barnes on 20161219 at 05:41 
20161220, 03:40  #39 
May 2007
Kansas; USA
2^{3}·3·5^{2}·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=10K25K. There are 31 k's remaining. Primes for n=10K25K: 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 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 Last fiddled with by gd_barnes on 20161220 at 03:41 
20161220, 06:10  #40 
May 2007
Kansas; USA
2^{3}·3·5^{2}·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<b1. D=b1 are the standard Riesel and Sierp conjectures at CRUS.
Last fiddled with by gd_barnes on 20161220 at 06:11 
20161220, 06:37  #41 
May 2007
Kansas; USA
27D8_{16} 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 20161220 at 06:38 
20161220, 17:54  #42  
Nov 2016
23×97 Posts 
Quote:
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) Last fiddled with by sweety439 on 20161220 at 17:58 

20170104, 16:39  #43  
Nov 2016
100010110111_{2} Posts 
Quote:
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 20170104 at 16:42 

20170105, 08:06  #44  
May 2007
Kansas; USA
2^{3}·3·5^{2}·17 Posts 
Quote:
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 largeconjectured base/digit combos that cannot be normally sieved at all. 

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