[seqfan] Re: Somebody knows this conjecture?

[Charles Greathouse]

See A101462.  It looks like the conjecture dates at least to 2005.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Jan 13, 2011 at 8:05 AM, Claudio Meller <claudiomeller at gmail.com> wrote:
> Somebody knows this conjecture?
>
> In the blog "Numeros y hojas de calculo"
> (http://hojaynumeros.blogspot.com/2011/01/alguien-sabe-algo-de-esto-1.html)
> the author, Antonio Roldán Martinez, asks if anybody knows
> about this conjecture : for any prime p exists a prime q such p+q=2^n.
>
> For example for p=2 q=2, for p=3 q=5, for p=5 q=3,for p=7 q= 549755813881,etc.
>
> The sequence a(n) = smallest prime q such p(n)+q = 2^n begins
> 2,5,3,549755813881,5,3,47,13,41,3,97,2011 this sequence is not in the
> OEIS.
> This sequence is similar to A096822.
> In this blog there is a table for p=2 to p= 211.
> For p=223, q =3705346855594118253554271520278013051304639509300498049262642688253220148477729,
> for p= 809, q=
>
> 285152538601387201165073225356268207805826781703034995661199532368704697950542336656619550707335712486165144348349650456918044045085964874890791332482638386765749667147516559380
> 179637015411927, etc.
>
> Is this a known conjecture?
> Is there is a theorem about this?
>
> Thank you
> --
> Claudio
>
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