Nash weight

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