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2006-04-25, 14:56   #78
Thomas11

Feb 2003

1,901 Posts

Due to the increasing interest on low-weight k, I'm releasing here some of the results I've got during the last 2-3 years. I've concentrated myself on the very-low weighted k.
The attached zip-file contains a list of more than 4500 k-values (up to k=238,000,000,000) with Nash weights equal to or below 15 -- all been tested for n=2-250,000 -- 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...
Attached Files
 LowNash15_with_primes.zip (51.8 KB, 125 views)

Last fiddled with by Thomas11 on 2006-04-25 at 15:01

 2006-04-25, 16:10 #79 edorajh     Oct 2003 Croatia 23×3×19 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 2006-04-25 at 16:13
2006-04-25, 17:43   #80
Thomas11

Feb 2003

1,901 Posts

Quote:
 Originally Posted by edorajh I'll pick following k... 59910449 380630849 442513453 ...
I should have added the note that some of the k of my list have already been tested much further, e.g. I have tested k=59910449 and 380630849 up to n=2M. And k=442513453 has been tested by myself to somewhere around n=2M and was later continued by Jean Penne.
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 2006-04-25 at 17:55

 2006-04-25, 19:16 #81 edorajh     Oct 2003 Croatia 23·3·19 Posts Ah, I see. In that case I would like to cancel my reservations.
 2006-04-26, 04:04 #82 VBCurtis     "Curtis" Feb 2005 Riverside, CA 3×113 Posts Thanks for the great source, Thomas. Since people (myself included) seem to like to search really low-weight k-values, I'll add some of the lowest-weight 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
 2006-04-26, 19:36 #83 Thomas11     Feb 2003 1,901 Posts I had been indeed two other "big" low-weight runs about 1-2 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 ------------------------------------------------ The second one, called "LowNash3", has reached n=500k and contains the following 32 k: 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 -- ------------------------------------------------ Both blocks have been sieved much higher, e.g. "LowNash2" has originally been prepared for nmax=2M, and "LowNash3" up to nmax=1M. 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 low-weight 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=1.1-2M range. And after that large gap for the "LowNash1" (e.g. no prime between n=1.25-2.27M), there should be one really soon... Last fiddled with by Thomas11 on 2006-04-26 at 19:37
2006-04-26, 19:48   #84
Thomas11

Feb 2003

76D16 Posts

I can provide you quite a few lists of low-weight k. The problem is that during my search for even lower weights I generated a few giga-bytes 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.
Attached Files
 Nash20.zip (204.1 KB, 135 views)

 2006-04-26, 19:54 #85 lsoule     Nov 2004 California 23·3·71 Posts I'm game! Sounds like the best way to get some mega-bit primes.
2006-04-26, 19:57   #86
Thomas11

Feb 2003

76D16 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.
Attached Files
 Nash30.zip (183.2 KB, 119 views)

2006-04-26, 19:59   #87
Thomas11

Feb 2003

1,901 Posts

Quote:
 Originally Posted by lsoule I'm game! Sounds like the best way to get some mega-bit primes.
Indeed! I've got 3 in 2004 between September and December...

2006-04-26, 20:11   #88
Thomas11

Feb 2003

1,901 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...
Attached Files
 Nash5.zip (48.7 KB, 133 views)

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