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New 18-tuplet

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  • jarek372000
    I have just found 3rd known (the largest known) prime 18-tuplet: Prime 18-tuplet 4530085223434265844952597 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42,
    Message 1 of 14 , Dec 13, 2008
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      I have just found 3rd known (the largest known) prime 18-tuplet:

      Prime 18-tuplet
      4530085223434265844952597 + d,
      d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
      (25 digits, Dec 14, 2008, Jaroslaw Wroblewski)

      The search has started on December 4. I am using up to 60 64-bit
      computers in students labs at Mathematical Institute of Wroclaw
      University (sometimes fewer if the are down or used by students).

      I estimate that I have deserved to find about 0.5-0.6 of an 18-tuplet
      by now, so I was a bit lucky. I will continue the search in hope for
      more 18-tuplets or for a miracle (19-tuplet).

      Jarek
    • Jens Kruse Andersen
      ... Congratulations on another impressive record! You now have all records for 15 to 21 simultaneous primes at http://hjem.get2net.dk/jka/math/simultprime.htm
      Message 2 of 14 , Dec 14, 2008
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        Jarek wrote:
        > I have just found 3rd known (the largest known) prime 18-tuplet:
        > 4530085223434265844952597 + d,
        > d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
        > (25 digits, Dec 14, 2008, Jaroslaw Wroblewski)

        Congratulations on another impressive record!
        You now have all records for 15 to 21 simultaneous primes at
        http://hjem.get2net.dk/jka/math/simultprime.htm

        It is actually the 4th known 18-tuplet including a trivial from 13 to 83.
        There are also trivial 19- to 23-tuplets with primes below 120.
        The first size with no known example is a 24-tuplet which I guess
        even you will not find for many years.

        --
        Jens Kruse Andersen
      • Mark Underwood
        ... Congratulations! It always amazes me to see primes at those densities at such large numbers. I wonder if future quantum computers (if such really are
        Message 3 of 14 , Dec 16, 2008
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          --- In primenumbers@yahoogroups.com, "jarek372000" <jaroslaw.wroblewski@...> wrote:
          >
          > I have just found 3rd known (the largest known) prime 18-tuplet:
          >
          > Prime 18-tuplet
          > 4530085223434265844952597 + d,
          > d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
          > (25 digits, Dec 14, 2008, Jaroslaw Wroblewski)
          >

          Congratulations! It always amazes me to see primes at those densities at such 'large'
          numbers. I wonder if future quantum computers (if such really are possible) would be able to
          find the yet unfound, probably monstrously sized 24 tuplets that Jens alluded to.

          Mark
        • jarek372000
          I just got another 18-tuplet: Prime 18-tuplet 11298510058634407483251313 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26
          Message 4 of 14 , Dec 17, 2008
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            I just got another 18-tuplet:

            Prime 18-tuplet
            11298510058634407483251313 + d,
            d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
            (26 digits, Dec 18, 2008, Jaroslaw Wroblewski)

            Jarek
          • jarek372000
            I just got another 18-tuplet: Prime 18-tuplet 23531820918273007548405133 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26
            Message 5 of 14 , Jan 15, 2009
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              I just got another 18-tuplet:

              Prime 18-tuplet
              23531820918273007548405133 + d,
              d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
              (26 digits, Jan 2009, Jaroslaw Wroblewski)

              Jarek
            • jarek372000
              I just got another prime 18-tuplet: 33755528632220819791319947 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 (26 digits, Jan
              Message 6 of 14 , Jan 25, 2009
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                I just got another prime 18-tuplet:

                33755528632220819791319947 + d,
                d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
                (26 digits, Jan 26, 2009, Jaroslaw Wroblewski)

                This is the largest known 18-tuplet and the largest known case of 18
                Simultaneous Primes.

                Jarek
              • Jens Kruse Andersen
                ... Congratulations! My ISP was bought and the buyer closed the old webhost last week. My former site at http://hjem.get2net.dk/jka has moved to
                Message 7 of 14 , Jan 26, 2009
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                  Jarek wrote:
                  > 33755528632220819791319947 + d,
                  > d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
                  > (26 digits, Jan 26, 2009, Jaroslaw Wroblewski)
                  >
                  > This is the largest known 18-tuplet and the largest known case of 18
                  > Simultaneous Primes.

                  and then:
                  > Here is the new AP19 with the smallest known start.
                  >
                  > 275525353 + 407133393*19#*n, n=0,..,18
                  > (Mariusz Szafranski, BOINC@Poland, Jaroslaw Wroblewski)

                  Congratulations!

                  My ISP was bought and the buyer closed the old webhost last week.
                  My former site at http://hjem.get2net.dk/jka has moved to
                  http://users.cybercity.dk/~dsl522332
                  File names are unchanged so all url's must just replace the start.
                  My email is unchanged.
                  The Largest Known Simultaneous Primes are now at
                  http://users.cybercity.dk/~dsl522332/math/simultprime.htm
                  Primes in Arithmetic Progression Records are at
                  http://users.cybercity.dk/~dsl522332/math/aprecords.htm
                  The pages are updated.

                  --
                  Jens Kruse Andersen
                • jarek372000
                  I just got another prime 18-tuplet: 44453357465442632103684223 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Feb 20,
                  Message 8 of 14 , Feb 19, 2009
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                    I just got another prime 18-tuplet:

                    44453357465442632103684223 + d,
                    d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
                    (26 digits, Feb 20, 2009, Jaroslaw Wroblewski)

                    This is the largest known 18-tuplet and the largest known case of 18
                    Simultaneous Primes.

                    Jarek
                  • Jens Kruse Andersen
                    ... Congratulations! An 18-tuplet is very impressive and this is your fifth. http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens
                    Message 9 of 14 , Feb 20, 2009
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                      Jarek wrote:
                      > 44453357465442632103684223 + d,
                      > d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
                      > (26 digits, Feb 20, 2009, Jaroslaw Wroblewski)
                      >
                      > This is the largest known 18-tuplet and the largest known case of 18
                      > Simultaneous Primes.

                      Congratulations!
                      An 18-tuplet is very impressive and this is your fifth.
                      http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

                      --
                      Jens Kruse Andersen
                    • jarek372000
                      I just got another prime 18-tuplet: 51342365971531191697537333 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Mar 11,
                      Message 10 of 14 , Mar 11 1:10 AM
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                        I just got another prime 18-tuplet:

                        51342365971531191697537333 + d,
                        d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
                        (26 digits, Mar 11, 2009, Jaroslaw Wroblewski)

                        This is the largest known 18-tuplet and the largest known case of 18
                        Simultaneous Primes.

                        Jarek
                      • Jaroslaw Wroblewski
                        I have just discovered the first known 27-digit prime 18-tuplet: 159272023128204753638724847 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60,
                        Message 11 of 14 , Jan 15, 2010
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                          I have just discovered the first known 27-digit prime 18-tuplet:

                          159272023128204753638724847 + d,
                          d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
                          (27 digits, Jan 15, 2010, Jaroslaw Wroblewski)

                          This is the largest known 18-tuplet and the largest known case of 18
                          Simultaneous Primes.

                          Jarek
                        • Jens Kruse Andersen
                          ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated with your 7th 18-tuplet record. -- Jens Kruse Andersen
                          Message 12 of 14 , Jan 15, 2010
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                            Jaroslaw Wroblewski wrote:
                            > 159272023128204753638724847 + d,
                            > d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
                            > (27 digits, Jan 15, 2010, Jaroslaw Wroblewski)
                            >
                            > This is the largest known 18-tuplet and the largest known case of 18
                            > Simultaneous Primes.

                            Congratulations!
                            http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated
                            with your 7th 18-tuplet record.

                            --
                            Jens Kruse Andersen
                          • jarek372000
                            I have just discovered another 27-digit prime 18-tuplet: Prime 18-tuplet 183837276562811649018077773 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48,
                            Message 13 of 14 , Apr 25, 2010
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                              I have just discovered another 27-digit prime 18-tuplet:

                              Prime 18-tuplet
                              183837276562811649018077773 + d,
                              d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
                              (27 digits, Apr 26, 2010, Jaroslaw Wroblewski)

                              This is the largest known 18-tuplet and the largest known case of 18
                              Simultaneous Primes.

                              Jarek
                            • Jens Kruse Andersen
                              ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen
                              Message 14 of 14 , Apr 26, 2010
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                                Jarek wrote:
                                > 183837276562811649018077773 + d,
                                > d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
                                > (27 digits, Apr 26, 2010, Jaroslaw Wroblewski)

                                Congratulations!
                                http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

                                --
                                Jens Kruse Andersen
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