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Nash weight

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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.


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.




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.


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