The final one is a bit different.

Since the Nash algorithm is quite slow when computing large ranges (e.g. millions) of k, one needs a faster tool. Therefore I implemented an ordinary sieve for p up to 512 and a smaller n range of only 1-1000. Due to precomputation of the "reversed orders of n" the whole calculation can be done in cache memory and is therefore really fast (e.g. about 3000 k/sec on a 1.7 GHz P4).

So one can use

**multi5** for a fast pre-scanning of a k-range and then do some sorting on the results and run the "good ones" through

**nash**.

For some historic reason it is written in Fortran (and lacks any comments) and there are no command line options. Therefore you need to edit the

*steer.txt* file for specifying the k-range and a print condition. The latter is necessary since otherwise the sieve would produce hundreds of megabytes of output within minutes...

The example

*steer.txt* file reads:

Code:

32000000025 KMIN
32001000000 KMAX
30 KSTEP
600 minimum weight for printing

You may skip the text comments at the right. The printing condition means, that the k is only printed when the weight is higher or equal to the specified value (e.g. weight>=600 in the example). Note, that we use a smaller n-range (1-1000), therefore 600 is a rather high weight. The weights are roughly one tenth of the Nash weights. Also note the restriction of k<2^63 (signed long).

Usage is simply:

for the example

*steer.txt* file you will get:

Code:

multi5
32000060235 609
32000107425 622
32000193225 612
32000315325 605
32000497485 640
32000553585 618
32000703735 674
32000816445 601
32000982585 622

If you want to store the results, you can simply redirect the output to a file, e.g.:

Of course it works the some way for

**nash** and

**mnash**...