Thread: Non 15k to 1M anyone? View Single Post
 2004-03-07, 13:01 #5 Thomas11     Feb 2003 27·3·5 Posts 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