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 2004-06-15, 17:54 #1 Citrix     Jun 2003 1,549 Posts Low Weight 15k Has anybody looked at these. These k might be low weight yet at the same time produce alot of primes. Thomas11 could I have a list of the 10 lowest weight 15 k's for analaysis. Just post them below. Thanks, Citrix
 2004-06-15, 18:57 #2 Thomas11     Feb 2003 2·3·317 Posts Citrix, currently I have only data on the 2145k's (=3*5*11*13) and 2805k's (=3*5*11*17) available, so here are lists of the 10 lowest weight 2145k's and 2805k's below k=2^32: Code:  2145k w w' 372683025 1093 1104 3215460105 1149 1153 3141118695 1201 1193 777573225 1204 1218 2700655815 1228 1207 1929064995 1237 1255 1231116315 1240 1270 1364059125 1240 1262 990267135 1244 1243 3608445555 1245 1253 2805k w w' 3463981455 1086 1090 3209063055 1181 1180 2759948895 1189 1193 1048545465 1198 1209 3640365465 1200 1208 2176391085 1223 1225 1545445605 1229 1217 693073425 1236 1231 321119205 1238 1233 759007755 1249 1250 w is the Nash weight for n=100001-110000, and w' is the Nash weight for n=1-10000. There is also some data on the lowest 15k's below k=500,000,000, but I need to uncompress and extract them out of the 8 GB data of Nash weights I have stored. Thomas11 Last fiddled with by Thomas11 on 2004-06-15 at 19:02
 2004-06-15, 19:15 #3 Thomas11     Feb 2003 2×3×317 Posts Citrix, thanks to bash and perl here is the list of the lowest weighted 15k's below k=550,000,000: Code:  k w w' 262477125 728 714 239956215 764 763 283239345 769 766 88432275 776 780 154105995 778 779 215186535 785 790 386590065 790 793 425396295 806 800 544720005 810 796 154546695 820 811 291749355 825 810 54757875 825 827 71734035 826 850 76846305 826 844 80330595 835 833 358627935 836 854 133922205 839 833 250508925 841 835 182327835 846 853 105756795 854 857 At all there are 335 15k's below k=550,000,000 which have Nash weights less than 1000. I may send you the complete list via email, if you like. -- Thomas11
 2004-06-15, 20:24 #4 Citrix     Jun 2003 1,549 Posts What about multiples of 105 and 3255? could you give me a list. Citrix
 2004-06-16, 07:02 #5 Kosmaj     Nov 2003 70468 Posts Thomas, if it's not a major problem for you can you kindly post Nash weights of all k's less than 300 or, for the beginning, those less than 100. k=53 appears to be so primeless, not a single prime between 43k and 183k.
 2004-06-16, 11:19 #6 Thomas11     Feb 2003 2×3×317 Posts Okay, here are the lowest 10 candidates for 105k and 3255k (k<550,000,000): Code:  105k w w' 302208375 1324 1333 280113645 1357 1359 441665805 1447 1444 524030325 1481 1460 520280565 1486 1473 469705215 1490 1476 302196405 1500 1477 395621415 1514 1516 498310155 1529 1497 254698395 1539 1522 Code:  3255k w w' 182634795 2019 2019 322378455 2040 2049 412607055 2052 2048 432651345 2064 2076 522808335 2064 2062 178670205 2067 2044 114032415 2083 2095 38893995 2088 2116 519156225 2135 2182 113355375 2144 2168 Kosmaj, I've posted the list for k<300 under the "Riesel numbers k<300" thread. -- Thomas11
 2004-06-17, 04:56 #7 Kosmaj     Nov 2003 2×1,811 Posts Thomas, thanks a lot! BTW, I searched for "Nash weight" by google and ran into this page about psieve by Chris Nash himself! Is this the right place to explore further? If you are aware of any other web page that can be useful please post below. Have you computed the weights using psive or by some other means?
 2004-06-17, 05:15 #8 Citrix     Jun 2003 1,549 Posts 302208375 has low wt and looks really good upto n=5000. I am searching it a bit higher. Primes so far. 302208375*2^39-1 302208375*2^44-1 302208375*2^69-1 302208375*2^69+1 - Twin - 302208375*2^80-1 302208375*2^139-1 302208375*2^145-1 302208375*2^188-1 302208375*2^199-1 302208375*2^339-1 302208375*2^364-1 302208375*2^375-1 302208375*2^376-1 - Sophie Germain - 302208375*2^376-1 302208375*2^375-1 - Sophie Germain - 302208375*2^535-1 302208375*2^1194-1 302208375*2^1480-1 edit: No primes upto 10000 so I stopped. Looks really god at first glance but it isn't. Non of the other low weight 15 K's look good either. 29 seems to be the best candidate to me to take to 10M. Citrix Last fiddled with by Citrix on 2004-06-17 at 05:26
2004-06-17, 11:13   #9
Thomas11

Feb 2003

2·3·317 Posts

Quote:
 Originally Posted by Kosmaj Thomas, thanks a lot! BTW, I searched for "Nash weight" by google and ran into this page about psieve by Chris Nash himself! Is this the right place to explore further? If you are aware of any other web page that can be useful please post below. Have you computed the weights using psive or by some other means?
There is another page by Joe McLean, which contains a lot of information:

http://www.glasgowg43.freeserve.co.uk/robintro.htm

And there is a Java applet by Jack Brennen, which uses Chris Nash's algorithm:

http://www.brennen.net/primes/ProthWeight.html

It computes weights for numbers of the form k*2^n+1, but it can handle the type k*2^n-1 too if you enter negative values of k.
You should note, that this applet computes the weights for n=1-10000 and scales them by a factor 1/1751.542 (1751.542 is something like an average weight).

For my own computations I wrote a small C program based on the algorithm Jack used in his Java applet. It uses the GMP library and works under several kinds of Unix (incl. Linux), but I never tried to compile it for Windows. I may send you the source code, if you want to give it a trial ...

-- Thomas11.

2004-06-17, 12:06   #10
ET_
Banned

"Luigi"
Aug 2002
Team Italia

112218 Posts

Quote:
 Originally Posted by Thomas11 There is another page by Joe McLean, which contains a lot of information: http://www.glasgowg43.freeserve.co.uk/robintro.htm And there is a Java applet by Jack Brennen, which uses Chris Nash's algorithm: http://www.brennen.net/primes/ProthWeight.html It computes weights for numbers of the form k*2^n+1, but it can handle the type k*2^n-1 too if you enter negative values of k. You should note, that this applet computes the weights for n=1-10000 and scales them by a factor 1/1751.542 (1751.542 is something like an average weight). For my own computations I wrote a small C program based on the algorithm Jack used in his Java applet. It uses the GMP library and works under several kinds of Unix (incl. Linux), but I never tried to compile it for Windows. I may send you the source code, if you want to give it a trial ... -- Thomas11.
I'd like to see the source too...

Luigi

2004-06-17, 12:36   #11
Thomas11

Feb 2003

2·3·317 Posts

Okay, here is the source code and a Linux binary too ...

Well, it's not much documented. You need to have a look into Jack's Java applet for documentation ...

To compile under Linux/Unix:

cc -O2 -o nash3 nash3.c -lgmp

To run:

nash3 <kmin> <kmax> <kstep>

example:

nash3 1 300 2

-- Thomas11.
Attached Files
 nash3.zip (6.7 KB, 177 views)

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