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Old 2007-01-05, 23:02   #9
jasong's Avatar
"Jason Goatcher"
Mar 2005

3×7×167 Posts

Originally Posted by masser View Post
You can use NewPGen to figure out some of the lowest Riesel/Sierpinski numbers. Use the "k*b^n+/1 with k fixed" sieves, and then use the "sieve until" option. Sieve up to p=1000 (or a million - something that doesn't take too long), and then have it update k and start again.

If this is done correctly, NewPGen will sieve k=1, 2, 3, and so on and create files 1.txt, 2.txt, 3.txt, etc. Sieve over a relatively small n set (1<=n<=2000) to keep the files small. Then just keep an eye on the size of the files - when you find one with size 0 - you've PROBABLY found a Riesel/Sierpinski number; do some fun math to figure out the covering set.

This method is sloppy, inefficient, etc.... but it's easy to set up and run. The alternative is to do some careful input file creation with PFGW or your own coding. There's also a tool (psieve is what I think it's called) out there for calculating the weights of certain sequences. I think it works for k*b^n+/-1, with bases other than 2. You can fix b and loop through many k values and then look for sequences with weight 0. Actually, now that I am thinking of it, this is probably the best way (without actually doing the math) to find the Sierpinski/Riesel numbers for other bases.

Hope this helps those of you interested...

best regards,
I'm going to try masser's idea and see how it goes for base-6. Just to make it official:

Reserving base-6 to try to find Riesel number.

Edit: Possibly stupid question, is there a simple way to search all the newpgen files in a directory and find the one with no values?

Edit2: NewPGen allows increasing n, but not k, so I'm I don't think it's possible to implement masser's idea without programming knowledge. Would be happy to be proven wrong.

Edit3: Reserving 14*8^n-1

Last fiddled with by jasong on 2007-01-05 at 23:09
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