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Re: Eleven successive primes not full period - is this a record?

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  • David Broadhurst
    ... Ah, Jens beat my case with 35, which was to be expected. David
    Message 1 of 12 , Aug 8, 2009
      --- In primenumbers@yahoogroups.com,
      "Jens Kruse Andersen" <jens.k.a@...> wrote:

      > > Any advance on 33 consecutive primes of this kind?
      >
      > [35, 1292613521, 1292614321]
      > [36, 2757553987, 2757554983]

      Ah, Jens beat my case with 35, which was to be expected.

      David
    • David Broadhurst
      ... [37, 7088772637, 7088772653] David
      Message 2 of 12 , Aug 8, 2009
        --- In primenumbers@yahoogroups.com,
        "Jens Kruse Andersen" <jens.k.a@> wrote:

        > [36, 2757553987, 2757554983]

        [37, 7088772637, 7088772653]

        David
      • David Broadhurst
        ... Whoops! The last of these 37 primes is 7088773519 n=37;p1=7088772637;v=vector(n);p=p1; for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
        Message 3 of 12 , Aug 8, 2009
          --- In primenumbers@yahoogroups.com,
          "David Broadhurst" <d.broadhurst@...> wrote:

          > [37, 7088772637, 7088772653]

          Whoops! The last of these 37 primes is 7088773519

          n=37;p1=7088772637;v=vector(n);p=p1;
          for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
          print([n,p1,p2,v]);

          [37, 7088772637, 7088773519,
          [2, 52, 2, 2, 2, 10, 4, 6, 2, 4, 2, 2, 2, 6, 2, 2, 8, 4,
          3, 2, 2, 3, 3, 60, 3, 2, 4, 35, 3, 4, 4, 3, 2, 25, 2, 2, 2]]

          With apologies for the typo,

          David
        • David Broadhurst
          ... 10 is not a primitive root of unity modulo any of the 40 consecutive primes beginning with 22588287443 n=40;p1=22588287443; v=vector(n);p=p1;
          Message 4 of 12 , Aug 8, 2009
            --- In primenumbers@yahoogroups.com,
            "David Broadhurst" <d.broadhurst@...> wrote:

            > 37, 7088772637, 7088773519

            10 is not a primitive root of unity modulo any of
            the 40 consecutive primes beginning with 22588287443

            n=40;p1=22588287443;
            v=vector(n);p=p1;
            for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
            print([n,p1,p2,v]);

            [40, 22588287443, 22588288409,
            [46, 15, 5, 2, 2, 5, 2, 2, 2, 2, 7, 2, 5, 9, 7, 30, 2, 4, 3, 3,
            3, 4, 3, 3, 2, 6, 2, 9, 2, 16, 2, 2, 2, 2, 2, 6, 48, 5, 2, 2]]

            David
          • David Broadhurst
            ... 10 is not a primitive root of unity modulo any of the 45 consecutive primes beginning with 24124140487 n=45;p1=24124140487; v=vector(n);p=p1;
            Message 5 of 12 , Aug 8, 2009
              --- In primenumbers@yahoogroups.com,
              "David Broadhurst" <d.broadhurst@...> wrote:

              > 10 is not a primitive root of unity modulo any of
              > the 40 consecutive primes beginning with 22588287443

              10 is not a primitive root of unity modulo any of
              the 45 consecutive primes beginning with 24124140487

              n=45;p1=24124140487;
              v=vector(n);p=p1;
              for(k=1,n,v[k]=(p-1)/znorder(Mod(10,p));p2=p;p=nextprime(p+1));
              print([n,p1,p2,v]);

              [45, 24124140487, 24124141903,
              [3, 2, 6, 2, 2, 90, 6, 3, 7, 4, 8, 3, 12, 4, 4,
              2, 2, 9, 20, 6, 7, 2, 4, 2, 36, 42, 2, 2, 2, 2,
              2, 2, 117, 10, 3, 15, 3, 4, 2, 2, 10, 2, 2, 2, 7]]

              David
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