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## Re: [PrimeNumbers] Primes of the form 2^p + p

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• I have just looked at 2^p-p and with the exception of p=2 this doesnt yield any primes p
Message 1 of 6 , Sep 6, 2004
I have just looked at 2^p-p
and with the exception of p=2 this doesnt yield any primes p<20000.
Clearly about half of the numbers of this form are divisible by 3 but I am sure there must be some more primes.
It might be an idea to look at covering sets like for the Sierpinski problem to see if a near covering set exists...
Gary

Cino

>From: Alan Eliasen <eliasen@...>
>To: Gary Chaffey <garychaffey2@...>
>CC: Peter Lesala <plesala@...>, primenumbers@yahoogroups.com
>Subject: Re: [PrimeNumbers] Primes of the form 2^p + p
>Date: Mon, 06 Sep 2004 00:59:09 -0600
>
>
> There are no more primes with p < 100000. This is a pretty interesting
>(and sparse) generator.

Try 4^p+p, 3^p+p+1, p^p+p+1, p^(p-1)/2 +p +1 etc. I am only finding a
couple. They are probably infinite in count maybe some one can prove on some
of these.

>
>
>Gary Chaffey wrote:
> > Hello Peter,
> > Yes there are some more primes of this form eg:-
> > 2^317+317
> > 2^701+701
> > There are no more with p<20000 though.
> > Regards
> > Gary
> >
> > Peter Lesala <plesala@...> wrote:
> > Hi,
> >
> > Very happy to rejoin the group after a long break. Pardon me I am out of
> > touch; and so the question I would like to ask may have been asked
>before.
see Sloanne's
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A057663
2^p - p is also in Sloanne's
> >
> > 2^3 + 3 = 11, prime
> > 2^5 + 5 = 37, prime
> > 2^89 + 89 is a probable prime (using PrimeForm).
> >
> > I tried a few more indeces higher than 9000, from the table of
>Mersenne's
> > primes, but did not find more primes of this form. Are there any more
>primes
> > of this form? ie
> >
> > 2^p + p, where p is a prime.
CLH

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