[seqfan] Somebody knows this conjecture?

[Claudio Meller]

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