A135485 and primes (and emirps) in A135485; New Prime Curio about 15013 by Post

Mon Feb 18 16:35:28 CET 2008

seconds to find a much larger...
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Message-ID: <5542af940802180902g345812ffrb1a9393a33ef2acb at mail.gmail.com>
Date: Mon, 18 Feb 2008 09:02:41 -0800
From: "Jonathan Post" <jvospost3 at gmail.com>
To: "Hans Havermann" <pxp at rogers.com>,
   "Stefan Steinerberger" <stefan.steinerberger at gmail.com>,
   "Ctibor O. Zizka" <ctibor.zizka at seznam.cz>
Subject: Re: A135485 and primes (and emirps) in A135485; New Prime Curio about 15013 by Post
Cc: seqfan at ext.jussieu.fr
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Thank you Hans, for re-confirming the result that Stefan Steinerberger
found, per my query. I'd asked if "primes in A135485" was worth
submitting.  njas emailed me to say that he didn't think so, hence I
submitted to Prime Curios instead.  I have no objection to Ctibor O.
Zizka having now submitted the same sequence, and I leave it to njas
to decide whether or not to show it is coauthored by myself and Ctibor
O. Zizka.

On 15 Feb 2008 I received the autoreply for the following form email
sent to Prime Curios:

To: editor
Subject: New Prime Curio about 82630...60939 (107-digits) by Post
From: Prime Curios! automailer for <jvospost3 at gmail.com>

   There has been a new curio submitted for your approval:

   82630...60939 (107-digits) [number_id=7553]

   This 107 digit prime is the sum from i = 1 to 47 of
   p(i)^(i-1), where p(i) is the i-th prime, = 2^0 + 3^1 + 5^2
   + 7^3 + 11^4 + ... + 211^46, since p(47) = 211. Note that
   47 is itself prime p(15), and 107 is the prime p(28).

   Stefan Steinerberger deserves credit as coauthor of this
   prime curio, and with complete search, found no bigger
   primes of this form with the index i running up to 1000.

   Reference:

   A135485 Sum_{i=1..n) p(i)^(i-1), where p(i)
   denotes i-th prime number.

    15013 [number_id=7550] 2^0 + 3^1 + 5^2 + 7^3 + 11^4
    = 15013 = Sum_{i=1..5) p(i)^(i-1).

    [Post]

On 2/18/08, Hans Havermann <pxp at rogers.com> wrote:
> On Feb 13, 2008, Jonathan Post wrote:
>
> > 2^0 + 3^1 + 5^2 + 7^3 + 11^4 = 15013 = Sum_{i=1..5) p(i)^(i-1), where
> > p(i) denotes i-th prime number, is the largest known such prime (as of
> > 13 Feb 2008)
>
> It's always a little dangerous submitting a "largest" on the basis of
> a small list. This one is very easy to program and it takes only a few
> seconds to find a much larger...
>
> 82630622945631213110177689366807452539856065087369361579159313857480591477585943781923604787789539375260939
>
> ...that is a probable prime: Sum(i=1..47) p(i)^(i-1)
>
>