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prime based sequence: father of the last sequence [Fwd: SEQ FROM Roger L. Bagula]

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  • Roger Bagula
    ... Subject: SEQ FROM Roger L. Bagula Date: Mon, 29 Sep 2003 22:15:22 -0400 (EDT) From: Reply-To: tftn@earthlink.net To:
    Message 1 of 6 , Sep 29, 2003
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      -------- Original Message --------
      Subject: SEQ FROM Roger L. Bagula
      Date: Mon, 29 Sep 2003 22:15:22 -0400 (EDT)
      From: <njas@...>
      Reply-To: tftn@...
      To: njas@...
      CC: tftn@...



      The following is a copy of the email message that was sent to njas
      containing the sequence you submitted.

      All greater than and less than signs have been replaced by their html
      equivalents. They will be changed back when the message is processed.

      This copy is just for your records. No reply is expected.
      Subject: NEW SEQUENCE FROM Roger L. Bagula


      %I A000001
      %S A000001 1,0,1,1,2,2,3,4,6,5,7,7,8,9,11,11,12,12,13,13,15,15,17,19,19,20,21,20,21,23,
      24,26,26,28,29,29,30,31,32,33,33,34,35,35,35,37,40,41,41,42,43,42,44,46,47,48,
      48,48,49,48,50,54,54,54,55,57,58,60,61,60,61,62,63,64,65,66,68,67,69,71,71,72,
      72,73,74,75,77,76,76,77,79,81,82,83,84,84,86,86,90,90,92,92,93,93,94,95,96,96,
      96,97,98,98,98,100,102,103,103,104,105,105,108,108,109,111,112,113,115,116,
      117,117,118,119,120,121,122,122,124,125,127,127,129,129,130,130,132,134,135,
      134,135,136,137,137,138,141,142,142,144,145,146,147,148,149,150,151,152,152,
      153,155,156,157,157,158,158,159,160,161,162,161,162,165,165,165,166,167,168,
      169,170,171,175,174,176,176,178,179,180,180,182,181,182
      %N A000001 A primes distribution difference from asymtotic sequence
      %C A000001 This sequence is extremely linear.
      %F A000001 a[n_]=-PrimePi[n]+Floor[Prime[n]/Log[n]]-2
      %t A000001 Digits=200
      a[n_]=-PrimePi[n]+Floor[Prime[n]/Log[n]]-2
      b=Table[a[n],{n,2,Digits}]
      %O A000001 2
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Sep 29 2003
      RH
      RA 209.179.241.6
      RU
      RI



      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/




      [Non-text portions of this message have been removed]
    • Zak Seidov
      This is copy of my post (sorry for those reading this twice): For p=11, minimal d = 4911773580 (OEIS A088430), and AP contains maximal number, 11, primes. For
      Message 2 of 6 , Sep 29, 2003
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        This is copy of my post
        (sorry for those reading this twice):

        For p=11,
        minimal d = 4911773580 (OEIS A088430),
        and AP contains maximal number, 11, primes.

        For p=13, d should be a factor of 2310.
        Who first find it (and then try 17,19,...)?
        Zak


        BTW I guess that found d is indeed minimal not unique-
        there is no reason of absense of other larger d's.


        On 28 Sep 2003, Russell E. Rierson wrote
        (http://www.mathforum.org/discuss/sci.math/m/133406/540774):
        >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and 19,
        >etc. These twins are only one unit apart.
        >
        >There are strings of prime numbers that are n-units apart:
        >
        >3, 5, 7, [3 prime numbers, 2 units apart]
        >
        >5, 11, 17, 23, 29, [5, 6 units]
        >
        >7, 157, 307, 457, 607, 757, 907, [7, 150 units]
        >
        >11... ? ...? ...? ...
        >
        >The question becomes: For all odd prime numbers P, are there P
        number of
        >primes that are the same numerical[equal] distance apart?
      • mad37wriggle
        By my calculation the smallest d for p=11 is 1536160080. Have I made a mistake? Richard
        Message 3 of 6 , Sep 30, 2003
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          By my calculation the smallest d for p=11 is 1536160080. Have I made a
          mistake?

          Richard


          --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
          wrote:
          > This is copy of my post
          > (sorry for those reading this twice):
          >
          > For p=11,
          > minimal d = 4911773580 (OEIS A088430),
          > and AP contains maximal number, 11, primes.
          >
          > For p=13, d should be a factor of 2310.
          > Who first find it (and then try 17,19,...)?
          > Zak
          >
          >
          > BTW I guess that found d is indeed minimal not unique-
          > there is no reason of absense of other larger d's.
          >
          >
          > On 28 Sep 2003, Russell E. Rierson wrote
          > (http://www.mathforum.org/discuss/sci.math/m/133406/540774):
          > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and 19,
          > >etc. These twins are only one unit apart.
          > >
          > >There are strings of prime numbers that are n-units apart:
          > >
          > >3, 5, 7, [3 prime numbers, 2 units apart]
          > >
          > >5, 11, 17, 23, 29, [5, 6 units]
          > >
          > >7, 157, 307, 457, 607, 757, 907, [7, 150 units]
          > >
          > >11... ? ...? ...? ...
          > >
          > >The question becomes: For all odd prime numbers P, are there P
          > number of
          > >primes that are the same numerical[equal] distance apart?
        • Ken Davis
          This is posted on behalf of richyfortythree cheers Ken ... 1536160080 is also what I get. (Same mistake maybe?) Cheers richyfourtythree ... made a ... 19,
          Message 4 of 6 , Sep 30, 2003
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            This is posted on behalf of
            richyfortythree
            cheers
            Ken
            > By my calculation the smallest d for p=11 is
            > 1536160080. Have I
            > made a
            > mistake?

            1536160080 is also what I get. (Same mistake maybe?)

            Cheers

            richyfourtythree


            --- In primenumbers@yahoogroups.com, "mad37wriggle"
            <fitzhughrichard@h...> wrote:
            >
            > By my calculation the smallest d for p=11 is 1536160080. Have I
            made a
            > mistake?
            >
            > Richard
            >
            >
            > --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
            > wrote:
            > > This is copy of my post
            > > (sorry for those reading this twice):
            > >
            > > For p=11,
            > > minimal d = 4911773580 (OEIS A088430),
            > > and AP contains maximal number, 11, primes.
            > >
            > > For p=13, d should be a factor of 2310.
            > > Who first find it (and then try 17,19,...)?
            > > Zak
            > >
            > >
            > > BTW I guess that found d is indeed minimal not unique-
            > > there is no reason of absense of other larger d's.
            > >
            > >
            > > On 28 Sep 2003, Russell E. Rierson wrote
            > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774):
            > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and
            19,
            > > >etc. These twins are only one unit apart.
            > > >
            > > >There are strings of prime numbers that are n-units apart:
            > > >
            > > >3, 5, 7, [3 prime numbers, 2 units apart]
            > > >
            > > >5, 11, 17, 23, 29, [5, 6 units]
            > > >
            > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units]
            > > >
            > > >11... ? ...? ...? ...
            > > >
            > > >The question becomes: For all odd prime numbers P, are there P
            > > number of
            > > >primes that are the same numerical[equal] distance apart?
          • Zak Seidov
            Yes, Richard and Ken, there is mistake - on my side, my d is larger than yours... Zak ... and
            Message 5 of 6 , Sep 30, 2003
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              Yes, Richard and Ken,
              there is mistake -
              on my side,
              my "d" is larger than yours...
              Zak

              --- In primenumbers@yahoogroups.com, "Ken Davis" <kraden@y...> wrote:
              > This is posted on behalf of
              > richyfortythree
              > cheers
              > Ken
              > > By my calculation the smallest d for p=11 is
              > > 1536160080. Have I
              > > made a
              > > mistake?
              >
              > 1536160080 is also what I get. (Same mistake maybe?)
              >
              > Cheers
              >
              > richyfourtythree
              >
              >
              > --- In primenumbers@yahoogroups.com, "mad37wriggle"
              > <fitzhughrichard@h...> wrote:
              > >
              > > By my calculation the smallest d for p=11 is 1536160080. Have I
              > made a
              > > mistake?
              > >
              > > Richard
              > >
              > >
              > > --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
              > > wrote:
              > > > This is copy of my post
              > > > (sorry for those reading this twice):
              > > >
              > > > For p=11,
              > > > minimal d = 4911773580 (OEIS A088430),
              > > > and AP contains maximal number, 11, primes.
              > > >
              > > > For p=13, d should be a factor of 2310.
              > > > Who first find it (and then try 17,19,...)?
              > > > Zak
              > > >
              > > >
              > > > BTW I guess that found d is indeed minimal not unique-
              > > > there is no reason of absense of other larger d's.
              > > >
              > > >
              > > > On 28 Sep 2003, Russell E. Rierson wrote
              > > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774):
              > > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17
              and
              > 19,
              > > > >etc. These twins are only one unit apart.
              > > > >
              > > > >There are strings of prime numbers that are n-units apart:
              > > > >
              > > > >3, 5, 7, [3 prime numbers, 2 units apart]
              > > > >
              > > > >5, 11, 17, 23, 29, [5, 6 units]
              > > > >
              > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units]
              > > > >
              > > > >11... ? ...? ...? ...
              > > > >
              > > > >The question becomes: For all odd prime numbers P, are there P
              > > > number of
              > > > >primes that are the same numerical[equal] distance apart?
            • Zak Seidov
              Russell sent me Phil s message with p=13 and p=17! Here is this message with my editings (sorry Phil!) %%%%%%% NMBRTHRY archives -- November 2001 (#9) Date:
              Message 6 of 6 , Oct 1, 2003
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                Russell sent me Phil's message with p=13 and p=17!
                Here is this message with my editings
                (sorry Phil!)

                %%%%%%%
                NMBRTHRY archives -- November 2001 (#9)
                Date: Wed, 7 Nov 2001 09:17:30 -0500
                Reply-To: Phil Carmody <fatphil@...>
                Sender: Number Theory List <NMBRTHRY@...>
                From: Phil Carmody <fatphil@...>
                Subject: Prime-producing Linear Polynomials
                The linear polynomial
                f(X) = dX+q
                can have at most q successive terms f(0)...f(q-1) prime, (and q must
                be prime for f(0) to be prime, evidently). It remains an open
                question, and one with few data-points, whether such maximal q-based
                q-length Arithmetic Progressions exist for every q.

                q=3, d=2 yield the primes 3,5,7;
                q=5, d=6 yield the primes 5,11,17,23,29;
                q=7, d=150 yield the primes 7,157,307,457,607,757,907.

                In 1986, Löh discovered for q=11 d=1536160080, and for q=13
                d=9918821194590.

                [The above was a synthesis of what Paulo Ribenboim has in The New Book
                of Prime Number Records]

                At the start of 2001 I started tackling the q=17 problem, and I wrote
                some brute force code to attack it. The code was peppered with bugs,
                and despite finding a record Cunningham Chain with the broken code
                http://listserv.nodak.edu/scripts/wa.exe?A2=ind0103&L=nmbrthry&P=R423
                I gave up both on the project and the code.

                However, I recently encountered other tasks which seemed like a good
                target for the code, and easier than the Arithmetic Progression
                problem, and resolved to de-mothball the code. Within a day of
                thinking this, Tom Hadley posted the very result I thought I might
                search for - a minimal 15-tuple ( http://www.ltkz.demon.co.uk/kt15.txt
                ). Rather than kill the idea, this encouraged me!

                So I (think I) fixed the bugs, and started the search again. After
                roughly 5 days on a single 533MHz Alpha (21164), I found the following
                result, finally toppling the 15-year-old record.

                The record is now
                q=17 d=341976204789992332560

                And the primes are
                <skip>

                q=19 anyone?

                (The scaling factors indicate that it might be possible with a
                collaborative effort, and my code parallelises)

                Thanks go to Tom Hadley for giving me a massive kick up the arse last
                week and to Paul Jobling who has been a useful resource on how to
                apply intelligence to brute force problems since the project began.

                Phil
                %%%%%%%%%%%%5


                --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
                wrote:
                > Yes, Richard and Ken,
                > there is mistake -
                > on my side,
                > my "d" is larger than yours...
                > Zak
                >
                > --- In primenumbers@yahoogroups.com, "Ken Davis" <kraden@y...>
                wrote:
                > > This is posted on behalf of
                > > richyfortythree
                > > cheers
                > > Ken
                > > > By my calculation the smallest d for p=11 is
                > > > 1536160080. Have I
                > > > made a
                > > > mistake?
                > >
                > > 1536160080 is also what I get. (Same mistake maybe?)
                > >
                > > Cheers
                > >
                > > richyfourtythree
                > >
                > >
                > > --- In primenumbers@yahoogroups.com, "mad37wriggle"
                > > <fitzhughrichard@h...> wrote:
                > > >
                > > > By my calculation the smallest d for p=11 is 1536160080. Have I
                > > made a
                > > > mistake?
                > > >
                > > > Richard
                > > >
                > > >
                > > > --- In primenumbers@yahoogroups.com, "Zak Seidov"
                <seidovzf@y...>
                > > > wrote:
                > > > > This is copy of my post
                > > > > (sorry for those reading this twice):
                > > > >
                > > > > For p=11,
                > > > > minimal d = 4911773580 (OEIS A088430),
                > > > > and AP contains maximal number, 11, primes.
                > > > >
                > > > > For p=13, d should be a factor of 2310.
                > > > > Who first find it (and then try 17,19,...)?
                > > > > Zak
                > > > >
                > > > >
                > > > > BTW I guess that found d is indeed minimal not unique-
                > > > > there is no reason of absense of other larger d's.
                > > > >
                > > > >
                > > > > On 28 Sep 2003, Russell E. Rierson wrote
                > > > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774):
                > > > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17
                > and
                > > 19,
                > > > > >etc. These twins are only one unit apart.
                > > > > >
                > > > > >There are strings of prime numbers that are n-units apart:
                > > > > >
                > > > > >3, 5, 7, [3 prime numbers, 2 units apart]
                > > > > >
                > > > > >5, 11, 17, 23, 29, [5, 6 units]
                > > > > >
                > > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units]
                > > > > >
                > > > > >11... ? ...? ...? ...
                > > > > >
                > > > > >The question becomes: For all odd prime numbers P, are there
                P
                > > > > number of
                > > > > >primes that are the same numerical[equal] distance apart?
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