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Old 2008-07-12, 20:14   #27
gd_barnes's Avatar
May 2007
Kansas; USA

132·61 Posts

Originally Posted by KEP View Post
The covering sets was copied directly from the output presented by the covering.exe program. Maybe I missunderstood and copied to much, but I decided to copy the entire amount of numbers, to make sure that you got what was needed.

Regarding base 252, it actually appears that k=1 is also very easily sieved. At n<=17426 I've completed 826 tests, and only 8 of these were for k=1 the remaining were for k=27.

Glad that you could use this work. Actually it's kind of need to have a thread were people can tell which bases they try to conjecture. However if I remember correctly, there is no way to verify PRPs for bases>255 (unless they are powers of 2?), so maybe we should encourage people to only work on bases <=255 for both Riesel or Sierpinski.

Take care.


The "exponent" that you are entering is too large on the covering software. On each base, start with an exponent of 4 and if no covering set found, go to an exponent of 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144 until you find a conjectured k. (Actually keep going after you find a conjectured k because you may find a slightly lower k with a larger covering set; although this is unlikely.)

Besides being the lowest conjectured k-value, the covering set needs to be the smallest number of factors that make the k-value always composite.

The "exponent" is the first value that you enter after typing "covering" to start the program.

To be blunt, you are wasting your time on k=1. It is mathematically proven that n must be a power of 2 because it is a GFN for all Sierp bases. Also, you don't need to test it to prove the conjecture. Just remove it from your sieved file. If you really want to test it for n>10K, all you need to do is test n=16384, 32768, 65536, 131072, 262144, and 524288 and TA-DA; you've now tested it all the way to n=1M (actually n=1048575) because the next test would be at n=1048576. In other words, at these high bases, you don't want to do even one test for high n-values that is a mathematically proven composite.

Getting into finding primes on GFN's is a whole other topic. There are several web pages (links are in the top-5000 site) dedicated to finding the primes and factors of them for various bases < 20 that can be generalized for all bases.

Edit: I wasn't aware that PRP's for bases > 256 that are not power of 2 could not be proven. If that is true then I agree, we need to keep bases that are not powers of 2 at < 256.


Last fiddled with by gd_barnes on 2008-07-12 at 20:25
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