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

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  • 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 1 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 2 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 3 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 4 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 5 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 6 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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