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Old 2006-04-25, 14:56   #78
Thomas11
 
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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
File Type: zip LowNash15_with_primes.zip (51.8 KB, 125 views)

Last fiddled with by Thomas11 on 2006-04-25 at 15:01
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Old 2006-04-25, 16:10   #79
edorajh
 
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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
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Old 2006-04-25, 17:43   #80
Thomas11
 
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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
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Old 2006-04-25, 19:16   #81
edorajh
 
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Ah, I see. In that case I would like to cancel my reservations.
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Old 2006-04-26, 04:04   #82
VBCurtis
 
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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
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Old 2006-04-26, 19:36   #83
Thomas11
 
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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
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Old 2006-04-26, 19:48   #84
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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
File Type: zip Nash20.zip (204.1 KB, 135 views)
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Old 2006-04-26, 19:54   #85
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I'm game! Sounds like the best way to get some mega-bit primes.
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Old 2006-04-26, 19:57   #86
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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.
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File Type: zip Nash30.zip (183.2 KB, 119 views)
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Old 2006-04-26, 19:59   #87
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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...
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Old 2006-04-26, 20:11   #88
Thomas11
 
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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
File Type: zip Nash5.zip (48.7 KB, 133 views)
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