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Difference between revisions of "Nash weight"

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(enhancement)
m (Fixing formatting and typos)
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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 < n < 110000 after performing a Nash sieve with a (default) exponent limit of 256.
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[[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 mathmatical info.}}
+
{{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}}.
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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 ''k''-value.
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It can be used for every sequence {{Kbn|k|b|n}} and {{Kbn|+|k|b|n}} without limitations of the {{Vk}}-value.
  
 
==Usage==
 
==Usage==
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==Enhancement==
 
==Enhancement==
A newer tool called "MNash" adds the possibilty to search for a k-range and also checks for special NashWeight ranges given.
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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.
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*[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/robinson weight?] at [[MersenneForum]]
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*[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 k- or Nash-Weight range to determine
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*[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
 
[[Category:Tools]]
 
[[Category:Tools]]

Revision as of 09:11, 23 September 2021

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 kbn-1 and kbn+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