2007-07-23, 05:31 | #1 |
"Jason Goatcher"
Mar 2005
DB3_{16} Posts |
Fun with the SOB and Riesel Sieve problem
I was thinking about the Riesel Sieve problem and how we're only considering odd ks. At the point we're at in the search, for any n we can find to make a k prime, it's trivial to extend that to any multiples of k that are still less than the Riesel number 509203.
Here's the thing, there are probably odd ks where the first n-value that yields a prime is so low that it doesn't cover the multiples. What I propose is that someone make a script that goes through the odd k up to 127,300, figures out how many times it would have to be multiplied by 2 to get a number bigger than 509203, and makes sure the n-value is at least that big. If it's smaller, then that number gets flagged. I know someone probably figured this out a long time ago, and maybe came up with a reason to dismiss the problem. But it's something to consider, the possibility that there may be a k that needs a prime and nobody has paid any attention because we're only worried about odd k. It would be fairly simple to test each number to n=19, to generate a file to run a script against; probably less trouble if we simply let the computer do a bit of unnecessary work in finding low primes. Would anybody be interested in trying this? I don't have the skills to make a script, or I'd do it myself. Oh, and it also extends to the Seventeen or Bust problem, which is the reason I included that in my subject line. :) |
2007-07-23, 06:29 | #2 |
Jun 2003
3·11·157 Posts |
See Sierpinski Problem and Riesel Number definitions. They are, by definition, limited to odd k's. A given (odd) k represents a whole series of integers (k.2^n+/-1, n>=1). If at least one prime is exhibited for the series, that's it, the k is not a Sierpinski/Riesel number. Multiples of k (by powers of 2) do NOT constitute a different series.
Last fiddled with by axn on 2007-07-23 at 06:30 |
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