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# Nash weight

## Explanation

Chris Nash gave a weight to show the number of remaining values of `k`•2^{n}+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`•2^{n}-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`•`b`^{n}-1 and `k`•`b`^{n}+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