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Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79

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  • James Merickel
    Addressing the question of why the particular number is not in OEIS is my preceding, and why it is not googlable (?) is down to how it is recorded at Prime
    Message 1 of 11 , Jul 30, 2013
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      Addressing the question of why the particular number is not in OEIS is my preceding, and why it is not googlable (?) is down to how it is recorded at Prime Curios! because of length (and is not elsewhere to my knowledge).
      --------------------------------------------
      On Mon, 7/29/13, Phil Carmody <thefatphil@...> wrote:

      Subject: Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79
      To: primenumbers@yahoogroups.com
      Date: Monday, July 29, 2013, 12:01 PM
















       











      On Mon, 7/29/13, James Merickel <moralforce120@...>
      wrote:

      > I am trying to add terms to http://oeis.org/A173189 ,
      which gives the number for

      > each integral base of primes obtainable by
      concatenating

      > numbers decremented in sequence from a power of the
      base

      > that are less than the smallest that is obtainable by

      > concatenating numbers increasing in sequence from a
      power of

      > the base. 



      """"

      In base n, the number of primes beginning with a power of n
      that are a concatenation of simply decremented numbers that
      are less than the smallest prime that is a similar
      concatenation beginning with a power of n and proceeding by
      increments instead.

      """



      Why does
      10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009

      not yield any hits on either OEIS or google?



      As it's a member of the sequence that your sequence is
      defined in terms of, one would expect that more primitive
      sequence to have been added first? Which would then enable
      you to simplify the horrendous description above.



      Phil

      --

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      [stolen with permission from Daniel B. Cristofani]
    • Phil Carmody
      ... Assuming fixed irrelevant base B, the number of candidates with up to d digits is approximately N_d = Sum{l=1..d} floor(d/l) Roughly the area under the
      Message 2 of 11 , Jul 30, 2013
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        > My little program to try to find a "forward concatenation prime"
        > in base 79 tells me that no such number exists below
        > exp(10000).
        >
        > Good luck finding one above that...  ;)

        Assuming fixed irrelevant base B, the number of candidates with up to d digits is approximately
        N_d = Sum{l=1..d} floor(d/l)
        Roughly the area under the hyperbola xy=d, 1<x<d
        Double d, and that area doubles.
        i.e at each individual digit length there's on average the same number of candidates.
        With density ~1/d. The sum of which diverges, so such a search isn't necessarily futile.

        However, given how slowly it diverges, one shouldn't hold out too much hope, as you say.

        Phil
        --
        () ASCII ribbon campaign () Hopeless ribbon campaign
        /\ against HTML mail /\ against gratuitous bloodshed

        [stolen with permission from Daniel B. Cristofani]
      • James Merickel
        The suggestion is now submitted as A227775 (in draft). ... On Tue, 7/30/13, James Merickel wrote: Subject: Re: [PrimeNumbers] seeking
        Message 3 of 11 , Jul 30, 2013
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          The suggestion is now submitted as A227775 (in draft).
          --------------------------------------------
          On Tue, 7/30/13, James Merickel <moralforce120@...> wrote:

          Subject: Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79
          To: primenumbers@yahoogroups.com, "Jack Brennen" <jfb@...>
          Date: Tuesday, July 30, 2013, 6:16 AM
















           









          Well, it's true that my (old) sequence is
          derivative of the one you describe; but a) mine is
          addressing the situation comparing an anomaly in base 10 as
          compared with others and b) I have been limited to just 3
          sequences in edit at one time at OEIS--with long delays--for
          a while so that thoughts of completeness of my work are kind
          of out the window (For examples, JKA pointed out a
          mis-titling of an entire large collection of sequences that
          were edited in (where the editors failed to note an
          ambiguity in meaning), and I have had no really good time to
          fix that or to add things like palindromic primes with index
          differing by (small) k from palindromic).



          Yes, is large, and I did not expect anybody to do this but
          thought I might ask. At any rate, as far as the sequence is
          concerned, b=79 has a very good chance of providing the 2nd
          largest value and possibly could overtake the value for
          b=10; and I appreciate any effort--successful or not--for
          this unusual question.



          JGM

          --------------------------------------------

          On Mon, 7/29/13, Jack Brennen <jfb@...>
          wrote:



          Subject: Re: [PrimeNumbers] seeking smallest 'forward
          concatenation prime' for power of 79

          To: primenumbers@yahoogroups.com

          Date: Monday, July 29, 2013, 2:15 PM

































           



















          My little program to try to find a "forward

          concatenation prime"



          in base 79 tells me that no such number exists below

          exp(10000).







          Good luck finding one above that... ;)







          By the way, I agree with Phil that the sequence of forward



          concatenation primes would seem to be much more
          fundamental



          than your derived sequence.







          On 7/29/2013 12:01 PM, Phil Carmody wrote:



          >



          > On Mon, 7/29/13, James Merickel <moralforce120@...>

          wrote:



          >> I am trying to add terms to http://oeis.org/A173189
          ,

          which gives the number for



          >> each integral base of primes obtainable by

          concatenating



          >> numbers decremented in sequence from a power of
          the

          base



          >> that are less than the smallest that is
          obtainable

          by



          >> concatenating numbers increasing in sequence from
          a

          power of



          >> the base.



          >



          > """"



          > In base n, the number of primes beginning with a
          power

          of n that are a concatenation of simply decremented
          numbers

          that are less than the smallest prime that is a similar

          concatenation beginning with a power of n and proceeding
          by

          increments instead.



          > """



          >



          > Why does

          10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009



          > not yield any hits on either OEIS or google?



          >



          > As it's a member of the sequence that your
          sequence

          is defined in terms of, one would expect that more
          primitive

          sequence to have been added first? Which would then enable

          you to simplify the horrendous description above.



          >



          > Phil



          >
        • djbroadhurst
          ... James logorrhea is utterly baffling, to me. I am usually able to understand definitions posted on this list, even when they are obfuscated. But the
          Message 4 of 11 , Jul 30, 2013
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            --- In primenumbers@yahoogroups.com,
            Phil Carmody <thefatphil@...> wrote:

            >> In base n, the number of primes beginning with a power of n
            >> that are a concatenation of simply decremented numbers that
            >> are less than the smallest prime that is a similar concatenation
            >> beginning with a power of n and proceeding by increments instead.
            >
            > simplify the horrendous description above

            James' logorrhea is utterly baffling, to me.
            I am usually able to understand definitions
            posted on this list, even when they are obfuscated.
            But the logorrheic convolution above defeats me.
            Only sharp minds, like Jack's, seem able to decode it.

            Please, Jack, might you give us lesser mortals some idea of
            what you have divined from James' verbiage?

            David
          • Jack Brennen
            I divined the lesser problem from the base 10 curiosity previously linked. Basically, take all of the positive integers that can be obtained by starting with
            Message 5 of 11 , Jul 30, 2013
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              I divined the "lesser problem" from the base 10 curiosity previously linked.

              Basically, take all of the positive integers that can be obtained
              by starting with a power of 10 and concatenating consecutive increasing
              numbers:

              10
              1011
              101112
              10111213
              1011121314
              100
              100101
              100101102
              1000
              10001001
              100010011002
              ...

              The smallest such prime is the 140 digit number linked as a prime
              curio in James' first post on this subject, consisting of the ten
              consecutive numbers from 10^13 to 10^13+9 concatenated.

              The fundamental question to this thread is to find the smallest such
              prime when operating in base 79. I assume that the trivial example
              of 10(base 79) is excluded, although it is prime.

              I ended up searching up to about 6500 decimal digits without finding
              such a prime.




              On 7/30/2013 3:53 PM, djbroadhurst wrote:
              >
              >
              > --- In primenumbers@yahoogroups.com,
              > Phil Carmody <thefatphil@...> wrote:
              >
              >>> In base n, the number of primes beginning with a power of n
              >>> that are a concatenation of simply decremented numbers that
              >>> are less than the smallest prime that is a similar concatenation
              >>> beginning with a power of n and proceeding by increments instead.
              >>
              >> simplify the horrendous description above
              >
              > James' logorrhea is utterly baffling, to me.
              > I am usually able to understand definitions
              > posted on this list, even when they are obfuscated.
              > But the logorrheic convolution above defeats me.
              > Only sharp minds, like Jack's, seem able to decode it.
              >
              > Please, Jack, might you give us lesser mortals some idea of
              > what you have divined from James' verbiage?
              >
              > David
              >
              >
              >
              > ------------------------------------
              >
              > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
              > The Prime Pages : http://primes.utm.edu/
              >
              > Yahoo! Groups Links
              >
              >
              >
              >
              >
            • James Merickel
              As noted, I have responded by submitting the suggested sequence to simplify this. I will point out that at least one OEIS editor apparently understood this.
              Message 6 of 11 , Jul 31, 2013
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                As noted, I have responded by submitting the suggested sequence to simplify this. I will point out that at least one OEIS editor apparently understood this. The change to the title may still be long; so, David, once you've figured out what I mean perhaps you will have better wording than the obvious change being made that refers to A227775.
                JGM
                --------------------------------------------
                On Tue, 7/30/13, djbroadhurst <d.broadhurst@...> wrote:

                Subject: [PrimeNumbers] Re: seeking smallest 'forward concatenation prime' for power of 79
                To: primenumbers@yahoogroups.com
                Date: Tuesday, July 30, 2013, 3:53 PM
















                 













                --- In primenumbers@yahoogroups.com,


                Phil Carmody <thefatphil@...> wrote:



                >> In base n, the number of primes beginning with a
                power of n

                >> that are a concatenation of simply decremented
                numbers that

                >> are less than the smallest prime that is a similar
                concatenation

                >> beginning with a power of n and proceeding by
                increments instead.

                >

                > simplify the horrendous description above



                James' logorrhea is utterly baffling, to me.

                I am usually able to understand definitions

                posted on this list, even when they are obfuscated.

                But the logorrheic convolution above defeats me.

                Only sharp minds, like Jack's, seem able to decode it.



                Please, Jack, might you give us lesser mortals some idea of


                what you have divined from James' verbiage?



                David
              • James Merickel
                I gather that Mr. Brennen meant the list to exclude powers of 10 from his remark on searching base 79, and this would be correct.
                Message 7 of 11 , Jul 31, 2013
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                  I gather that Mr. Brennen meant the list to exclude powers of 10 from his remark on searching base 79, and this would be correct.

                  --- On Tue, 7/30/13, Jack Brennen <jfb@...> wrote:

                  > From: Jack Brennen <jfb@...>
                  > Subject: Re: [PrimeNumbers] Re: seeking smallest 'forward concatenation prime' for power of 79
                  > To: "djbroadhurst" <d.broadhurst@...>
                  > Cc: primenumbers@yahoogroups.com
                  > Date: Tuesday, July 30, 2013, 5:46 PM
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >  
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  >
                  > I divined the "lesser problem" from the
                  > base 10 curiosity previously linked.
                  >
                  >
                  >
                  > Basically, take all of the positive integers that can be
                  > obtained
                  >
                  > by starting with a power of 10 and concatenating consecutive
                  > increasing
                  >
                  > numbers:
                  >
                  >
                  >
                  > 10
                  >
                  > 1011
                  >
                  > 101112
                  >
                  > 10111213
                  >
                  > 1011121314
                  >
                  > 100
                  >
                  > 100101
                  >
                  > 100101102
                  >
                  > 1000
                  >
                  > 10001001
                  >
                  > 100010011002
                  >
                  > ...
                  >
                  >
                  >
                  > The smallest such prime is the 140 digit number linked as a
                  > prime
                  >
                  > curio in James' first post on this subject, consisting
                  > of the ten
                  >
                  > consecutive numbers from 10^13 to 10^13+9 concatenated.
                  >
                  >
                  >
                  > The fundamental question to this thread is to find the
                  > smallest such
                  >
                  > prime when operating in base 79. I assume that the trivial
                  > example
                  >
                  > of 10(base 79) is excluded, although it is prime.
                  >
                  >
                  >
                  > I ended up searching up to about 6500 decimal digits without
                  > finding
                  >
                  > such a prime.
                  >
                  >
                  >
                  > On 7/30/2013 3:53 PM, djbroadhurst wrote:
                  >
                  > >
                  >
                  > >
                  >
                  > > --- In primenumbers@yahoogroups.com,
                  >
                  > > Phil Carmody <thefatphil@...> wrote:
                  >
                  > >
                  >
                  > >>> In base n, the number of primes beginning with
                  > a power of n
                  >
                  > >>> that are a concatenation of simply decremented
                  > numbers that
                  >
                  > >>> are less than the smallest prime that is a
                  > similar concatenation
                  >
                  > >>> beginning with a power of n and proceeding by
                  > increments instead.
                  >
                  > >>
                  >
                  > >> simplify the horrendous description above
                  >
                  > >
                  >
                  > > James' logorrhea is utterly baffling, to me.
                  >
                  > > I am usually able to understand definitions
                  >
                  > > posted on this list, even when they are obfuscated.
                  >
                  > > But the logorrheic convolution above defeats me.
                  >
                  > > Only sharp minds, like Jack's, seem able to decode
                  > it.
                  >
                  > >
                  >
                  > > Please, Jack, might you give us lesser mortals some
                  > idea of
                  >
                  > > what you have divined from James' verbiage?
                  >
                  > >
                  >
                  > > David
                  >
                  > >
                  >
                  > >
                  >
                  > >
                  >
                  > > ------------------------------------
                  >
                  > >
                  >
                  > > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                  >
                  > > The Prime Pages : http://primes.utm.edu/
                  >
                  > >
                  >
                  > > Yahoo! Groups Links
                  >
                  > >
                  >
                  > >
                  >
                  > >
                  >
                  > >
                  >
                  > >
                  >
                  >
                  >
                  >
                  >
                  >
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