20081224, 21:15  #1 
"Phil"
Sep 2002
Tracktown, U.S.A.
1120_{10} Posts 
Paper on Sierpinski problems just published
A paper on the Sierpinski problem currently under investigation by Seventeen or Bust, the dual Sierpinski problem, and the intersection of these two problems has just been published by INTEGERS: The Electronic Journal of Combinatorial Number Theory. The paper, entitled "Resolution of the Mixed Sierpinski Problem" and authored by Louis Helm, Phil Moore, Payam Samidoost, and George Woltman is available here. (Scroll down to paper A61.) The main result is the theorem that 78557 is the smallest positive odd integer k such that both k*2^n+1 and k+2^n are composite for any positive integer n. One section describes previously unpublished innovations by George to algorithms to do computations modulo numbers of the form k*2^n+/c with k>1 that are of immediate utility to Seventeen or Bust, the Riesel problem investigation, and several other related projects on this forum. Some amusing estimates of the prospects of eventually solving either the original Sierpinski problem or the dual problem are also given.
Last fiddled with by philmoore on 20110406 at 20:39 Reason: broken mirror link deleted 
20090410, 21:47  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
2^{5}·5·7 Posts 
Here is a link to some PowerPoint slides I used in a talk I gave yesterday called "Prime, Perfect, and Sierpinski Numbers" here at Lane Community College, where I teach. It starts out with a bit of history, then goes from there into a bit about Sierpinski numbers and Riesel numbers. It was definitely a fun lecture to deliver.
http://www.lanecc.edu/fpd/documents/...oquium_000.ppt Last fiddled with by philmoore on 20090414 at 04:19 
20090410, 22:50  #3  
Jun 2003
Ottawa, Canada
10010010101_{2} Posts 
Quote:
Last fiddled with by philmoore on 20090414 at 04:20 

20090410, 23:02  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
I wasn't going to post this since it's not too significant, but if it's going to be in flash or something else, might as well mention it: slide 26 has the wrong exponent for the largest known Mersenne (46... instead of 43...).

20090410, 23:59  #5 
"Phil"
Sep 2002
Tracktown, U.S.A.
2^{5}·5·7 Posts 
Thanks for the correction, I'll make the change!
Last fiddled with by philmoore on 20090413 at 23:19 Reason: Replaced with corrected version, 13 April. 
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