number theory question

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3 total messages Started by Paul Bruckman Sat, 26 Sep 1998 00:00

#1242

Author: Paul Bruckman
Date: Sat, 26 Sep 1998 00:00

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What can be said about the following propositions?

1)  Given d = 2,3,... , there exist primes p and q with p-q=2d , q+2
composite .

2)  Given d = 1,2,..., there exist primes p and q with q-p=2d, q+2
composite.

Is either (1) or (2) a theorem, and if so, can you supply references?
If not, can they be proved?  And if the proofs are not known, has
anybody else thought of this problem (again, references are sought)?

Thank you in advance for your consideration.  Sincerely, Paul Bruckman

Re: number theory question

#1243

Author: bobs
Date: Mon, 28 Sep 1998 00:00

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In article <6uj62q$fi8$1@news-1.news.gte.net>,
  aardwolf@gte.net wrote:
> What can be said about the following propositions?
>
> 1)  Given d = 2,3,... , there exist primes p and q with p-q=2d , q+2
> composite .
>
> 2)  Given d = 1,2,..., there exist primes p and q with q-p=2d, q+2
> composite.
>
> Is either (1) or (2) a theorem, and if so, can you supply references?
> If not, can they be proved?

For each d, whether there exists primes p,q   such that p-q = 2d is an open,
unsolved problem.

Of course it is true.  We just have no proof.

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Re: number theory question

#1241

Author: Werner Aumayr
Date: Tue, 29 Sep 1998 00:00

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See also:
http://www.utm.edu/research/primes/notes/conjectures/


[Moderator's note: the original poster has written again to ask that
 responses also be sent directly to him at   aardwolf@gte.net  ]

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