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

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  • Phil Carmody
    ... 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
    Message 1 of 11 , Jul 29 12:01 PM
    • 0 Attachment
      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
      --
      () ASCII ribbon campaign () Hopeless ribbon campaign
      /\ against HTML mail /\ against gratuitous bloodshed

      [stolen with permission from Daniel B. Cristofani]
    • Jack Brennen
      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
      Message 2 of 11 , Jul 29 2:15 PM
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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... ;)

        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
        >
      • James Merickel
        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
        Message 3 of 11 , Jul 30 6:16 AM
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          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

          >
        • 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 4 of 11 , Jul 30 6:19 AM
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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

            --

            () ASCII ribbon campaign () Hopeless ribbon
            campaign

            /\ against HTML mail /\ against
            gratuitous bloodshed



            [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 5 of 11 , Jul 30 10:08 AM
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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 6 of 11 , Jul 30 1:44 PM
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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 7 of 11 , Jul 30 3:53 PM
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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 8 of 11 , Jul 30 5:46 PM
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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 9 of 11 , Jul 31 8:53 AM
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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 10 of 11 , Jul 31 9:01 AM
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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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