- Cino

>From: Alan Eliasen <eliasen@...>

Try 4^p+p, 3^p+p+1, p^p+p+1, p^(p-1)/2 +p +1 etc. I am only finding a

>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.

couple. They are probably infinite in count maybe some one can prove on some

of these.

>

see Sloanne's

>

>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.

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A057663

2^p - p is also in Sloanne's> >

CLH

> > 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.

- 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@...>

Try 4^p+p, 3^p+p+1, p^p+p+1, p^(p-1)/2 +p +1 etc. I am only finding a

>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.

couple. They are probably infinite in count maybe some one can prove on some

of these.

>

see Sloanne's

>

>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.

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A057663

2^p - p is also in Sloanne's> >

CLH

> > 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.

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