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Old 2004-06-15, 17:54   #1
Citrix
 
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Default 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
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Old 2004-06-15, 18:57   #2
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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
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Old 2004-06-15, 19:15   #3
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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
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Old 2004-06-15, 20:24   #4
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What about multiples of 105 and 3255? could you give me a list.

Citrix
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Old 2004-06-16, 07:02   #5
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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.
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Old 2004-06-16, 11:19   #6
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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
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Old 2004-06-17, 04:56   #7
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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?
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Old 2004-06-17, 05:15   #8
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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
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Old 2004-06-17, 11:13   #9
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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.
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Old 2004-06-17, 12:06   #10
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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
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Old 2004-06-17, 12:36   #11
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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
File Type: zip nash3.zip (6.7 KB, 177 views)
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