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 2008-02-01, 20:24 #1 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 2×5×599 Posts Prime test 3^n-2 is there a program that will prime test numbers of the form 3^n-2 there is probibably a really simple answer for this but i have searched and can only find that pfgw and prp will do prp tests on these numbers
 2008-02-02, 08:15 #2 paulunderwood     Sep 2002 Database er0rr 11·383 Posts http://tech.groups.yahoo.com/group/p...m/message/8626 is the latest news I could find. This is no low hanging fruit here. Primo will prove some larger ones if you run it for long enough. http://primes.utm.edu/prove/index.html (Why do most search engines seem to screw up with "^" and "-" -- another topic for discussion. ) Last fiddled with by paulunderwood on 2008-02-02 at 08:21
2008-02-03, 05:17   #3
jasong

"Jason Goatcher"
Mar 2005

3×7×167 Posts

Quote:
 Originally Posted by henryzz is there a program that will prime test numbers of the form 3^n-2 there is probibably a really simple answer for this but i have searched and can only find that pfgw and prp will do prp tests on these numbers
It is possible to prove numbers of the form k*b^n+c if b>|c| .

The proof is forthcoming, just not by me.

2008-02-03, 12:28   #4
victor

Oct 2005
Fribourg, Switzerlan

22·32·7 Posts

Quote:
 Originally Posted by jasong It is possible to prove numbers of the form k*b^n+c if b>|c| .
It is possible to prove numbers of any form.

 2008-02-03, 17:23 #5 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 2·5·599 Posts if u r prepared 2 spend years
2008-02-04, 06:36   #6
jasong

"Jason Goatcher"
Mar 2005

3×7×167 Posts

Quote:
 Originally Posted by henryzz if u r prepared 2 spend years
No, I'm talking about something similar to the LLR test.

He's working on a paper that deals with this stuff. Apparently, if you have a complete understanding of how and why the LLR test works, then the expansion(or whatever the correct word is) is trivially proven.

Unfortunately, a lot of this stuff confuses me from square one, so "trivially proven" ends up being the same as "totally undecipherable."

 2008-02-04, 07:31 #7 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 135468 Posts same here
2008-02-04, 11:52   #8
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

33·239 Posts

Quote:
 Originally Posted by paulunderwood http://tech.groups.yahoo.com/group/p...m/message/8626 is the latest news I could find. This is no low hanging fruit here. Primo will prove some larger ones if you run it for long enough. http://primes.utm.edu/prove/index.html (Why do most search engines seem to screw up with "^" and "-" -- another topic for discussion. )
Since x+2 is distressingly non-cyclotomic (and, therefore, you can't (except by enormous luck and elliptic curves, at which point you're doing ECPP) find algebraic groups defined mod p of order p+2), I presume that there isn't a clever algorithm like the Lucas-Lehmer or Proth tests in this situation, and you're reduced to general-purpose methods.

I'd be happy to be shown to be wrong

 2008-02-04, 17:45 #9 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 135468 Posts i was just wondering because it would speed things up a lot i half thought the answer would be no
2008-02-04, 19:34   #10
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22·5·373 Posts

Quote:
 Originally Posted by henryzz i was just wondering because it would speed things up a lot i half thought the answer would be no
I am not sure that I understand the antecedant of the word "it", in the above
sentence. Can you explain further?

Are you speculating whether a Lucas-Lehmer type test exists for numbers of
the form 3^n - 2??? Although we do not have a proof that such a test is
impossible, there are good reasons for believing so.

 2008-02-08, 17:31 #11 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 2·5·599 Posts the it means having a method yes i was hoping for a lucas lehmer like test i didnt really expect one was possible though

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