# [seqfan] Re: Somebody knows this conjecture?

David Wilson davidwwilson at comcast.net
Sat Jan 15 05:54:32 CET 2011

```The conjecture is false.

For p = 509203, we have p+q = 2^n => q is divisible by one of 3, 5, 7, 13,
17 or 241.

Any other prime in A101306 is also a counterexample.

In fact, this problem is the Riesel problem in disguise.

----- Original Message -----
From: "RGWv" <rgwv at rgwv.com>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Friday, January 14, 2011 1:08 AM
Subject: [seqfan] Re: Somebody knows this conjecture?

?Et al,

In the first 1000 primes, I have found values for all terms but 4;
unknown values at: 286, 341, 530 & 591 and they exceed 35000. I will let
this run over night. I will be sending into the OEIS a b-text file tomorrow.

Bob.

-----Original Message-----
From: Claudio Meller
Sent: Thursday, January 13, 2011 5:48 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Somebody knows this conjecture?

Yes Charles, is the same sequence.
Thank you, Claudio

2011/1/13 Charles Greathouse <charles.greathouse at case.edu>

> 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
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Claudio
http://grageasdefarmacia.blogspot.com
http://todoanagramas.blogspot.com/
http://simplementenumeros.blogspot.com/

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