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Re: [PrimeNumbers] private reply Re: Prime 19-tuplet

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  • Jens Kruse Andersen
    ... Up to 10^12 there are 4 cases of more than 17 consecutive decades with exactly one prime. The first case has 20 but not in two centuries : 22497123000+n,
    Message 1 of 37 , Jul 19, 2011
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      woodhodgson wrote:
      > While the matter of "centuries" is around again, I have another
      > rather idle question regarding centuries that have exactly 10 primes,
      > with an even distribution of 1 prime per decade - ie 1 prime in each
      > of the following intervals:
      >
      > [100n+1,100n+9], [100n+11,100n+19], [100n+21,100n+29], ...,
      > [100n+91,100n+99].

      Up to 10^12 there are 4 cases of more than 17 consecutive decades
      with exactly one prime.

      The first case has 20 but not in two "centuries":
      22497123000+n, for n = 391, 409, 419, 427, 437, 449, 457, 461,
      479, 487, 499, 503, 511, 529, 533, 547, 559, 563, 577, 581

      The second case has 19:
      70739860000+n, for n = 2917, 2929, 2931, 2943, 2959, 2967, 2979, 2989,
      2997, 3001, 3013, 3027, 3039, 3049, 3057, 3069, 3079, 3087, 3093

      The third case has 22 and includes two consecutive "centuries":
      479808685000+n, for n = 481, 493, 501, 513, 529, 537, 549, 553, 567,
      579, 583, 597, 607, 613, 621, 637, 649, 651, 667, 673, 687, 691

      The fourth case is the first with exactly 18:
      806416924000+n, for n = 447, 459, 463, 471, 483, 493, 507,
      517, 529, 531, 541, 559, 561, 571, 583, 597, 603, 613

      --
      Jens Kruse Andersen
    • Jens Kruse Andersen
      ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen
      Message 37 of 37 , Dec 31, 2012
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        Jaroslaw Wroblewski wrote:
        > Here is 5th known large prime 19-tuplet:
        >
        > 2406179998282157386567481191 + d,
        > d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
        > (28 digits, Dec 2012, Raanan Chermoni & Jaroslaw Wroblewski)
        >
        > This sets new records for 18 and 19 Simultaneous Primes.

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

        --
        Jens Kruse Andersen
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