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Old 2004-03-07, 13:01   #5
Thomas11
 
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Feb 2003

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Hi Joss and Masser,

thank's for your interest. First of all I should note that I'm currently out of town for about one week. Therefore I haven't full access to all the data I'd like to provide to you.

For the Nash weight computation I used a small C program written by myself after a "close" look into John Brennen's Java applet. I developed my program in a UNIX environment using the GMP library. I compiled and used it under Linux too, but I don't know if GMP is available for Windows and how to get it compiled there. Nevertheless, if some of you are interested, I could send you the source code and/or Linux binary.

Please don't ask for a "complete" list of Nash weights for all (odd) k's up to 350 million. Since my program stores the results into ascii files this would be 3.5 GByte of data (10.5 MByte per 1 million range of k's = 500.000 odd k's)! But any small portion of data can be easily extracted for the list, e.g. the "less than 100" list or a "larger than 6000" list or a "zero weight" list (= Riesel numbers). The "less than 100" list would be about 900 kByte (or 300 kByte ZIPed).

Originally I had planned to take one or a few k's up to 10M and I did a lot of sieving work in that direction. But after all it is too much work for one single person having only a few machines. So any of you may take part in the search for some big primes ...

The following 23 k values have been sieved for n=2..10.000.000 up to p=8.000.000.000.000 (yes, 8 trillion!) and already LLR-tested up to n=1.000.000:

Code:
      k      w    w'   prime for n=
-----------------------------------------
  19370947   17   15        25
  59910449   15   15        92
  80857169   19   17         4
 143316643   15   16   
 162405629   20   21       896, 12236
 175437131   20   21
 189030223   18   19
 203012861   16   17       754
 209826493   16   18
 224371169   17   17      3548
 243163663   15   18    919087
 245265883   16   17
 260213857   13   16
 265831619   19   16
 276278983   16   18     21623, 473423
 290851087   23   21        57
 298095191   14   15
 300871183   22   23
 308120317   19   19
 308141737   19   19      7517
 315940139   18   17      8388, 595620
 326840893   17   15        31
----------------------------------------
(w is the "original" Nash weight for n=100.001-110.000,
while w' is the Nash weight obtained for n=1-10.000)
I have no idea, which k should be choosen for testing n>1 million. Maybe one or a few for which no prime exists for n<1 million.

As I already mentioned, I don't have access to the presieved ranges at the moment, but I can send them to Joss around March 15th, so he could store the data on 15k.org.

It should be mentioned that a single LLR test on a n=1 million number takes about 4 hours on a 2.4 GHz P4. And around n=1.5 million the time raises to 8 hours and more.

In case you can't wait until I've sent you the presieved data and/or you want to test some untested k-values for lower n, here is a short list of low weight k's which I haven't tested so far (but someone else may have tested them):

Code:
      k      w    w'  
----------------------
  10013593   40   46
  10247561   38   38
  10284899   27   30
  10346561   46   48
  10453199   28   26
  10463923   34   28
  10598947   45   45
  10639619   37   38
  10671431   34   36
  10805593   49   45
  10813783   34   40
  10906603   38   38
  10932097   44   41
  10943321   50   61
  11223059   26   27
  11311003   31   28
  11319193   45   43
  11468609   46   47
  11639819   39   38
  11658187   48   44
  11716993   48   41
  11741347   42   44
  11846279   50   48
  11847299   45   45
  11932211   38   37
  11955659   36   36
  12254533   36   36
  12305981   44   44
  12334093   49   53
  12551291   43   41
  12695159   31   36
  12753311   48   42
  12825793   49   53
  13277471   48   50
  13651423   48   49
  13768087   46   49
  13900807   23   18
  14085941   35   36
  14321533   29   23
  14466883   40   41
  14533213   42   44
  14549347   48   52
  14745343   31   32
  14961487   25   23
----------------------
I suggest to sieve them for n=2..250.000 up to about p=10 or 15 billion. Only 150-400 candidates will remain per k and can be LLR tested in a few hours. Candidates for n<256 should be tested by Pari (or Mathematica, Maple, etc.) rather than using LLR, since it may crash or report a prime as "non-prime".
There should be quite a few primes in the above list for n<250.000 but only
one or two Top5000 primes.

Best wishes and a few primes ...

Thomas
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