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Old 2016-12-18, 18:58   #34
sweety439
 
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base 11, d=6: Tested to 470000, I still found no such k.
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Old 2016-12-18, 19:12   #35
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We need updates at 15 minute intervals. You are getting sloppy -- too few updates!
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Old 2016-12-18, 19:12   #36
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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
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Old 2016-12-19, 05:06   #37
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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
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Old 2016-12-19, 05:32   #38
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Default 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
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Old 2016-12-20, 03:40   #39
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Default 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
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Old 2016-12-20, 06:10   #40
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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<b-1. D=b-1 are the standard Riesel and Sierp conjectures at CRUS.

Last fiddled with by gd_barnes on 2016-12-20 at 06:11
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Old 2016-12-20, 06:37   #41
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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
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Old 2016-12-20, 17:54   #42
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Quote:
Originally Posted by sweety439 View Post
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
File Type: txt base-4-digit-1.txt (796 Bytes, 73 views)
File Type: txt base-9-digit-1.txt (32 Bytes, 68 views)
File Type: txt base-9-digit-8.txt (235 Bytes, 52 views)
File Type: txt base-12-digit-1.txt (730 Bytes, 71 views)
File Type: txt base-12-digit-E.txt (2.3 KB, 52 views)

Last fiddled with by sweety439 on 2016-12-20 at 17:58
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Old 2017-01-04, 16:39   #43
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Quote:
Originally Posted by gd_barnes View Post
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
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Old 2017-01-05, 08:06   #44
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Quote:
Originally Posted by sweety439 View Post
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.
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