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Old 2008-02-01, 20:24   #1
henryzz
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Default 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
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Old 2008-02-02, 08:15   #2
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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
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Old 2008-02-03, 05:17   #3
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Quote:
Originally Posted by henryzz View Post
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.
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Old 2008-02-03, 12:28   #4
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Quote:
Originally Posted by jasong View Post
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.
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Old 2008-02-03, 17:23   #5
henryzz
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if u r prepared 2 spend years
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Old 2008-02-04, 06:36   #6
jasong
 
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Quote:
Originally Posted by henryzz View Post
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."
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Old 2008-02-04, 07:31   #7
henryzz
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same here
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Old 2008-02-04, 11:52   #8
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Quote:
Originally Posted by paulunderwood View Post
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
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Old 2008-02-04, 17:45   #9
henryzz
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i was just wondering because it would speed things up a lot
i half thought the answer would be no
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Old 2008-02-04, 19:34   #10
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Quote:
Originally Posted by henryzz View Post
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.
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Old 2008-02-08, 17:31   #11
henryzz
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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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