Choose your own K and work on finding a top-5000 prime!

[gd_barnes]

Originally Posted by Happy5214

Funny you mention that. I had started work on that k in late February, but I had suspended work on my local PRPNet servers for a bit in March to work on the GIMPS PRP-CF-DC backlog. I have since resumed work on both clients. That k is currently at n=288k, and I should get to n=300k by the end of this week. You can take over from there.

OK I'll start testing within a couple of days for n=300k-500k. Thanks.

[gd_barnes]

k=14549535 is complete for n=300K-500K, 5 primes were found shown below, the k is released. Happy is still working on a double-check for n=125K-300K.

Primes:
14549535*2^376607-1
14549535*2^390393-1
14549535*2^430198-1
14549535*2^446171-1
14549535*2^453217-1

[Happy5214]

The aforementioned double-check of k=14549535 for n=125k-300k is complete. In addition to the known primes, the following new primes were found:

• 14549535*2^149070-1
• 14549535*2^160953-1
• 14549535*2^161852-1
• 14549535*2^180548-1
• 14549535*2^199042-1
• 14549535*2^204177-1

[gd_barnes]

k=8847:

Double-check complete to n=500K. No problems found.

Hole filled for n=500K-700K. In addition to confirming the 3 previously found primes, one additional prime was found:
8847*2^514298-1

Results attached.

[gd_barnes]

k=32767:

This one is currently reserved by Diep for n=5M-30M. Since it is so low weight I thought it would be interesting to see if there were any more primes up to n=1M.

Double-check complete to n=50K. 4 previously found primes confirmed. No problems found.

First-time check complete for n=50K-1M. No primes found.

This is a very low-weight k! :-)

Results attached.

[Happy5214]

As of May 9, the (near-)Woodall k's listed in https://www.mersenneforum.org/showpo...&postcount=363 have been completed to n=475k. The following primes were found:

• 667071*2^450745-1
• 938237*2^455888-1
• 667071*2^465478-1
• 582833*2^467596-1

[gd_barnes]

k=10005 has a large prime gap so I double-checked it for n=0-1.25M.

34 primes confirmed; no problems found.

Results attached.

[Happy5214]

I've completed the remaining RPS 9th and 10th Drive k's with missing ranges from n=350k to 375k. 21 primes were found, which are attached. Of the laptops mentioned in my last post on this set of k's, the Kubuntu Focus has been dedicated to GIMPS and is not working on this project, but the older laptop is actively working on this. The expected finish date is currently October, though I may dedicate some additional cycles to it once it gets closer to the finish line.

[gd_barnes]

Back about 13-14 years ago Beyond (SB2) did a lot of searching on many low-weight k's. Although he gave details about what he was working on his details were frequently incomplete and he did not complete a lot of what he was sieving. One of the main issues is that we never knew where he started his searches. Sometimes they started at n=1, other times at n=300K, many times we never knew. I found these 4 main status posts of his:

post link / date
https://www.mersenneforum.org/showpost.php?p=100670 2007-03-13
https://www.mersenneforum.org/showpost.php?p=101240 2007-03-18
https://www.mersenneforum.org/showpost.php?p=110378 2007-07-14
https://www.mersenneforum.org/showpost.php?p=153292 2008-12-14

I took all of the k's found in those posts and removed some k's that were already checked by others since then. This left 98 k's all of which are shown below.

All 98 k's have been double-checked by me for n=1 to 1M. 5 missing primes were found for ranges that he said were done and 13 new primes were found for ranges that he sieved but never searched or failed to report.

Missing primes:
9613*2^734907-1
124679*2^12-1
239857*2^161901-1
334147*2^103669-1
36231101*2^34482-1

New primes:
273613*2^397407-1
313979*2^243184-1
412843*2^107943-1
412843*2^142983-1
412843*2^377223-1
434729*2^941408-1
451049*2^281984-1
464909*2^136620-1
469933*2^330667-1
473279*2^103840-1
700477*2^492061-1
783073*2^402635-1
1034503*2^174283-1

All k's searched with all primes listed below.
Red = missing
Bold = new

k / n-primes
2039:     24, 64, 319920, 841312
2171:     14, 202, 1594, 6754, 101974
2279:     900, 6572, 23772, 35252
2591:     134, 326, 830, 2174, 17270
2741:     50, 138, 1610, 1850, 3954, 10202, 23178, 84858, 468594, 737586
2759:     388, 405820, 569812
2797:     21, 6093, 7389, 9861
2983:     11, 671, 767, 2891, 771455
3343:     483, 1299
3389:     92, 848, 2684, 23864, 209996, 504584, 749828
3539:     12, 192, 4236, 869868
3817:     40381, 161197, 218917
3821:     70, 15814, 439006
3823:     7, 287, 335, 599, 1015, 2407, 384223
4327:     13, 37, 133, 1189
4597:     17, 37, 161, 221, 721, 112009, 799781
4813:     515, 11379, 13155
5077:     117, 333, 490629, 881829
5099:     184, 1216, 9936, 19072, 27648
5323:     27, 83, 8651, 107643
6119:     4544, 678080
7331:     34, 87154, 704842
9179:     4120, 10408, 41680
9613:     1479, 34239, 464439, 636159, 734907
9913:     1187, 8387
10949:    1492, 1516
11519:    164444
12791:    2818, 29398, 308026
17077:    677
19919:    888, 2688, 8460, 170820
21547:    1, 121, 2233, 16001, 310625, 936473
21673:    7, 775, 129175
22183:    727, 2471, 773447
24067:    1753, 2069, 2881, 700073
24671:    1290, 2250, 11698, 108906, 382066
25229:    238652
30727:    1121, 3353, 15929
43541:    507098, 850394
48973:    43, 115, 259, 32119
65279:    1640, 4952, 66632, 625704
70079:    1428
106303:   1939
114613:   211, 1687, 461551
117037:   1029
124679:   12, 948, 2460, 10308, 497244, 769908
132217:   15281
171607:   21117, 73245
179743:   99731
192509:   52
236377:   19693, 111973, 178285, 824773
239857:   33, 7233, 161901
248047:   11613
249127:   5189, 31301
273613:   39, 87, 159, 397407
278713:   17159, 57719
279731:   1782
284579:   56, 4736
294907:   545, 203921, 221409
306251:   22, 29038, 37462
313979:   4, 184, 243184
320107:   41, 257, 8249
323563:   243, 9099
332159:   4416
334147:   37, 7981, 103669
334331:   78, 294, 7998
362737:   153
370421:   201442
384029:   24
403993:   379
412843:   15, 16047, 107943, 142983, 377223
434729:   8, 20, 80, 941408
441907:   837, 42861
451049:   7748, 22784, 281984
464353:   191, 527, 1919, 371279
464909:   73740, 136620
465187:   3949, 16441
469933:   51, 330667
473279:   160, 92032, 103840
492787:   553, 1865, 6961, 58849
516569:   20
648433:   75
700477:   973, 492061
780427:
783073:   11, 402635
808477:   11673
842711:   226, 3034, 3754            
844559:
893887:   257
1005449:  204, 41100
1034503:  43, 5971, 174283
1210421:  28674, 655938
10013593: 3847
10108837: 33657
10247561: 730
10284899: 868, 2596
10346561: 32714
36231101: 34482, 469002
37616317:

Karsten, this cleans up a former mess of k's, many of which need to be entered into the Wiki but couldn't because their accuracy was in question. I will slowly work on getting them all into the Wiki going in descending order from the largest k. Larger k's have less history and so are easier to enter. I will be referencing Beyond's work, my own current and former work, the old low-weight stats page done by Joss, and other misc. work that has popped up by other people or projects that I find from searches on the k's in this forum including work done by NPLB for k=2000-3000.

Attached are primes and residues from the effort.

Gary

[Happy5214]

The (near-)Woodall k's listed in https://www.mersenneforum.org/showpo...&postcount=363 have been completed to n=500k. The following primes were found:

• 197673*2^475399-1
• 1467763*2^480087-1
• 665127*2^483394-1
• 1268979*2^485869-1
• 1268979*2^487073-1
• 665127*2^488224-1
• 938237*2^491576-1
• 1183953*2^496687-1

I want to reiterate my reservation of k=454483, which will resume work from this point.