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

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  • Gary Chaffey
    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
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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<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...


      >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
      see Sloanne's
      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
      > > primes, but did not find more primes of this form. Are there any more
      > > of this form? ie
      > >
      > > 2^p + p, where p is a prime.

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