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Difference between revisions of "Nash weight"
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==Explanation== | ==Explanation== | ||
| − | [[Chris Nash]] gave a weight to show the number of remaining values of {{Kbn|+|k|n}} after sieving the range 100000 < | + | [[Chris Nash]] gave a weight to show the number of remaining values of {{Kbn|+|k|n}} after sieving the range 100000 < {{Vn}} < 110000 after performing a Nash sieve with a (default) exponent limit of 256. |
| − | {{C|red|Need a deeper | + | {{C|red|Need a deeper mathematical info.}} |
A later definition was also done for {{Kbn|k|n}}. | A later definition was also done for {{Kbn|k|n}}. | ||
| Line 9: | Line 9: | ||
The nash tool for Windows-based systems can be found [https://www.mersenneforum.org/showpost.php?p=358591&postcount=13 here] written by [[Thomas Ritschel]]. | The nash tool for Windows-based systems can be found [https://www.mersenneforum.org/showpost.php?p=358591&postcount=13 here] written by [[Thomas Ritschel]]. | ||
| − | It can be used for every sequence {{Kbn|k|b|n}} and {{Kbn|+|k|b|n}} without limitations of the | + | It can be used for every sequence {{Kbn|k|b|n}} and {{Kbn|+|k|b|n}} without limitations of the {{Vk}}-value. |
==Usage== | ==Usage== | ||
| Line 39: | Line 39: | ||
==Enhancement== | ==Enhancement== | ||
| − | A newer tool called "MNash" adds the | + | A newer tool called "MNash" adds the possibility to search for a {{Vk}}-range and also checks for special NashWeight ranges given. |
Download the tool [https://www.mersenneforum.org/showpost.php?p=421186&postcount=19 here] including some examples. | Download the tool [https://www.mersenneforum.org/showpost.php?p=421186&postcount=19 here] including some examples. | ||
| Line 45: | Line 45: | ||
*[http://irvinemclean.com/maths/nash.htm Explanation and results] | *[http://irvinemclean.com/maths/nash.htm Explanation and results] | ||
*[http://www.brennen.net/primes/ProthWeight.html ProthWeight], Java applet by Jack Brennen | *[http://www.brennen.net/primes/ProthWeight.html ProthWeight], Java applet by Jack Brennen | ||
| − | *[https://www.mersenneforum.org/showthread.php?t=11844 How to calculate Nash/ | + | *[https://www.mersenneforum.org/showthread.php?t=11844 How to calculate Nash/Robinson weight?] at [[MersenneForum]] |
*[https://www.mersenneforum.org/showthread.php?t=2645 Low Weight 15k] at [[MersenneForum]] | *[https://www.mersenneforum.org/showthread.php?t=2645 Low Weight 15k] at [[MersenneForum]] | ||
| − | *[https://www.mersenneforum.org/showthread.php?t=7213 some tools for weights computing...] at [[MersenneForum]] including "MNash.exe" for a | + | *[https://www.mersenneforum.org/showthread.php?t=7213 some tools for weights computing...] at [[MersenneForum]] including "MNash.exe" for a {{Vk}}- or Nash-Weight range to determine |
*[https://www.mersenneforum.org/showthread.php?t=18818 Nash weight of base 17] at [[MersenneForum]] including the used version described above | *[https://www.mersenneforum.org/showthread.php?t=18818 Nash weight of base 17] at [[MersenneForum]] including the used version described above | ||
| + | *[https://github.com/happy5214/nash Updated version of above sources] on GitHub | ||
[[Category:Tools]] | [[Category:Tools]] | ||
Latest revision as of 15:50, 19 August 2024
Explanation
Chris Nash gave a weight to show the number of remaining values of k•2n+1 after sieving the range 100000 < n < 110000 after performing a Nash sieve with a (default) exponent limit of 256.
Need a deeper mathematical info.
A later definition was also done for k•2n-1.
Download
The nash tool for Windows-based systems can be found here written by Thomas Ritschel.
It can be used for every sequence k•bn-1 and k•bn+1 without limitations of the k-value.
Usage
Typing
nash
will show some help:
nash - a tool for computing Nash weights for sequences k*b^n+-1 usage: nash <k> <b> or: nash <k> If no base <b> is given, b=2 is assumed. By default Proth sequences (k*b^n+1) are assumed. For Riesel sequences (k*b^n-1) enter k as -k. Example (computing the Nash weight for 14*17^n-1): nash -14 17 -14 17 803 800 The first two values are k and b, the third value (803) is the standard Nash weight for the interval 100000 <= n < 110000. The forth value is the Nash weight for 0 <= n < 10000.
Enhancement
A newer tool called "MNash" adds the possibility to search for a k-range and also checks for special NashWeight ranges given.
Download the tool here including some examples.
External links
- Explanation and results
- ProthWeight, Java applet by Jack Brennen
- How to calculate Nash/Robinson weight? at MersenneForum
- Low Weight 15k at MersenneForum
- some tools for weights computing... at MersenneForum including "MNash.exe" for a k- or Nash-Weight range to determine
- Nash weight of base 17 at MersenneForum including the used version described above
- Updated version of above sources on GitHub
