20060425, 14:56  #78 
Feb 2003
2^{7}·3·5 Posts 
Due to the increasing interest on lowweight k, I'm releasing here some of the results I've got during the last 23 years. I've concentrated myself on the verylow weighted k.
The attached zipfile contains a list of more than 4500 kvalues (up to k=238,000,000,000) with Nash weights equal to or below 15  all been tested for n=2250,000  together with the primes I've found. The different weights are explained at the bottom of the list. I hope that you will find the data somewhat useful for your own studies...  Thomas P.S.: And just feel free to pick some of these k to test them beyond n=250,000... Last fiddled with by Thomas11 on 20060425 at 15:01 
20060425, 16:10  #79 
Oct 2003
Croatia
2^{3}·3·19 Posts 
Wow! This is real treasure! Thanks a lot for sharing this with us.
I'll pick following k... 59910449 380630849 442513453 535224337 536864983 811064503 953992993 1529129471 1545102311 1918825267 Initially, I'll test them from n=250k to n=1M, and after that will continue up to n=2M, and possibly even further, at least some of them. Last fiddled with by edorajh on 20060425 at 16:13 
20060425, 17:43  #80  
Feb 2003
2^{7}×3×5 Posts 
Quote:
k=535224337, 536864983, 811064503 have also been tested somewhat further. I'll need to look into my records. Nevertheless, everything above k=1,000,000,000 should be available (e.g. at least those k haven't been tested by me any further  this means all but k=59493015971). You should also check www.15k.org before wasting your cpu(s)...  Thomas Last fiddled with by Thomas11 on 20060425 at 17:55 

20060425, 19:16  #81 
Oct 2003
Croatia
2^{3}·3·19 Posts 
Ah, I see. In that case I would like to cancel my reservations.

20060426, 04:04  #82 
"Curtis"
Feb 2005
Riverside, CA
2^{2}·1,321 Posts 
Thanks for the great source, Thomas. Since people (myself included) seem to like to search really lowweight kvalues, I'll add some of the lowestweight work to 15k webpage.
If you have time/energy, send or post another zip of work completed above n=250,000, so we avoid duplication. curtis 
20060426, 19:36  #83 
Feb 2003
11110000000_{2} Posts 
I had been indeed two other "big" lowweight runs about 12 years ago.
The first one, which I call "LowNash2", has reached n=1.1M and contains the following 36 k (together with the primes I found): Code:
overall nmax tested: 1100000 k primes  389152177  410314627  414322661 2114 432043439  443200949  463395913  482987411  491362811  493412999  494660219  531115657  535224337  536864983  540196717  552455201 25862 564510097 11345 567143683 4027 578625847  589877983  609937687 1561 651488009 156, 10956 660879671 702 667868189  673503191  691459721  713633533  725433403  738297163  759833699  801584081 182 811064503  814419757  835596479  851324377  855686399 162836 857656417 4953  Code:
overall nmax tested: 500000 k primes  253104569 348 255333787 21 257250883 326, 9359, 74879, 109919 257878177  260334281  264039239  268346437 156061 270274153  272294801  273507613  279599587  280970467  287742253  289797523 115, 45619, 256435 291996611 350058 294660907 37, 901, 35653, 52741, 362773 307715767  307876003  315419827  316203817  316371073  323063771 205578, 219114 324539233 35, 155, 90035, 136475 325434251 2050 332827783 103, 125383 332847659 89828 334490381 7382, 36902, 127478 338381947  340130729  343172617  346694111  348970301   I'm currently digging out those old sieve files and want to take them further. In principle "LowNash3" has already reached the optimal sieve depth to be LLR tested up to n=1M, and I'm planning to combine it with the 31 k values I reported on earlier this week. "LowNash2" still needs about one or two weeks to reach it's optimal sieve depth for testing up to n=2M. But testing all the 36 k by myself would be very demanding. So, one could think of a distributed attack, e.g. the "3rd RPS drive". And then, there are the 23 k values (I call them the "original LowNash" or "LowNash1") which already have reached n=2.27M (< note this as a status report). I spent thousands of hours for sieving them, e.g. they are preparated for n up to 10M, and the sieve is around n=14T. These k are already well prepared for LLR testing them into the million digit region (which start around n=3.3M). This could also be taken as the "3rd drive". So, just let me know, if there is some interest in a distributed lowweight search. I already suggest such project about two years ago, but there wasn't any reply. Nevertheless, I'm still willing to prepare the necessary input data for either case. In principle, this could be an easy way for finding a megabit prime. But, of course, there is no guarantee that the ranges contain any prime at all. Nevertheless, I'm still quite confident that there is at least one prime for "LowNash2" in the n=1.12M range. And after that large gap for the "LowNash1" (e.g. no prime between n=1.252.27M), there should be one really soon... Last fiddled with by Thomas11 on 20060426 at 19:37 
20060426, 19:48  #84 
Feb 2003
2^{7}·3·5 Posts 
I can provide you quite a few lists of lowweight k. The problem is that during my search for even lower weights I generated a few gigabytes of raw data, which obviously cannot be distributed through the internet. And the raw data wouldn't be very useful to someone else.
So I generated a few files, which are hopefully of some interest for you: First of all, there a file of 32314 k (up to 400,000,000,000) which have Nash weights up to 20. Note again, that some of the lower k have already been investigated by myself or others. So check www.15k.org before duplicating work. 
20060426, 19:54  #85 
Nov 2004
California
2^{3}·3·71 Posts 
I'm game! Sounds like the best way to get some megabit primes.

20060426, 19:57  #86 
Feb 2003
1920_{10} Posts 
The second file is for Nash weights up to 30. Due to the filesize limitations this is only up to k=50,000,000,000.

20060426, 19:59  #87  
Feb 2003
780_{16} Posts 
Quote:


20060426, 20:11  #88 
Feb 2003
2^{7}·3·5 Posts 
The following file is for "real" experts only!
It contains k of Nash weights up to 5. These are very big k (up to 17 digits). This means that you'll need to use ksieve. The chances are very, very low to find any prime at all. Probably quite a few of them are Riesel numbers, e.g. they will never produce a prime. But, nevertheless, these kind of numbers can be tested beyond n=1M quite easily, since typically only about 100 candidates per million (or even less) survive the sieve... 
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