Loading ...
Sorry, an error occurred while loading the content.

seeking smallest 'forward concatenation prime' for power of 79

Expand Messages
  • James Merickel
    Dear groupmembers: I am trying to add terms to http://oeis.org/A173189 , which gives the number for each integral base of primes obtainable by concatenating
    Message 1 of 11 , Jul 29, 2013
    • 0 Attachment
      Dear groupmembers:

      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.

      For b=79, the smallest number of values (including the start) that may be concatenated from a power of 79 with increments used that is not certain to give a composite because of divisibility by a small prime is 22, and values that are a concatenation of an allowable number of numbers in sequence this way only arise around once every 11 orders of magnitude (powers of 10). So, the value I seek may be prohibitively large and appears to certainly be with what I have been using to find it. If anybody is inclined to try and obtains a result, I would be interested (and will either note due credit in COMMENTS at the above sequence or not do so if that is requested if I continue and find the value belonging there for base 79 (or the person may wish to do his or her own edit)).

      So, if anybody can find it, I am looking for the base-79 analogue to the value http://primes.utm.edu/curios/page.php?number_id=10049. Described, not with all digits shown. Thanks if this might be accomplished.

      JGM
    • 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 2 of 11 , Jul 29, 2013
      • 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 3 of 11 , Jul 29, 2013
        • 0 Attachment
          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 4 of 11 , Jul 30, 2013
          • 0 Attachment
            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 5 of 11 , Jul 30, 2013
            • 0 Attachment
              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 6 of 11 , Jul 30, 2013
              • 0 Attachment
                > 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 7 of 11 , Jul 30, 2013
                • 0 Attachment
                  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 8 of 11 , Jul 30, 2013
                  • 0 Attachment
                    --- 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 9 of 11 , Jul 30, 2013
                    • 0 Attachment
                      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 10 of 11 , Jul 31, 2013
                      • 0 Attachment
                        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 11 of 11 , Jul 31, 2013
                        • 0 Attachment
                          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
                          >
                          > >
                          >
                          > >
                          >
                          > >
                          >
                          > >
                          >
                          > >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                          >
                        Your message has been successfully submitted and would be delivered to recipients shortly.