20040615, 17:54  #1 
Jun 2003
1,579 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 
20040615, 18:57  #2 
Feb 2003
2^{2}·3^{2}·53 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 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 20040615 at 19:02 
20040615, 19:15  #3 
Feb 2003
2^{2}×3^{2}×53 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  Thomas11 
20040615, 20:24  #4 
Jun 2003
3053_{8} Posts 
What about multiples of 105 and 3255? could you give me a list.
Citrix 
20040616, 07:02  #5 
Nov 2003
2×1,811 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. 
20040616, 11:19  #6 
Feb 2003
1908_{10} 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  Thomas11 
20040617, 04:56  #7 
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? 
20040617, 05:15  #8 
Jun 2003
1,579 Posts 
302208375 has low wt and looks really good upto n=5000. I am searching it a bit higher. Primes so far.
302208375*2^391 302208375*2^441 302208375*2^691 302208375*2^69+1  Twin  302208375*2^801 302208375*2^1391 302208375*2^1451 302208375*2^1881 302208375*2^1991 302208375*2^3391 302208375*2^3641 302208375*2^3751 302208375*2^3761  Sophie Germain  302208375*2^3761 302208375*2^3751  Sophie Germain  302208375*2^5351 302208375*2^11941 302208375*2^14801 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 20040617 at 05:26 
20040617, 11:13  #9  
Feb 2003
1908_{10} Posts 
Quote:
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^n1 too if you enter negative values of k. You should note, that this applet computes the weights for n=110000 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. 

20040617, 12:06  #10  
Banned
"Luigi"
Aug 2002
Team Italia
3×1,601 Posts 
Quote:
Luigi 

20040617, 12:36  #11 
Feb 2003
3564_{8} 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. 
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