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[PrimeNumbers] Re: 870, 12, 3, 2

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  • Jens Kruse Andersen
    I returned to this after completing some other tasks. 320572022166380880 +/- 30 +/- 9 +/- 5 +/- 3 gives 16 distinct consecutive primes. They can also be
    Message 1 of 8 , Dec 1, 2008
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      I returned to this after completing some other tasks.

      320572022166380880 +/- 30 +/- 9 +/- 5 +/- 3 gives 16 distinct
      consecutive primes. They can also be written:
      320572022166380880 +/- n, for n = 13, 19, 23, 29, 31, 37, 41, 47.

      It is the shared second tightest admissible pattern for
      16 distinct primes produced by the additive combinations of
      5 numbers where the largest is always added.
      The 37 tightest patterns were searched to some limit.
      4 of them had a case with 16 primes but only one case had
      consecutive primes.
      The 5 numbers, the difference between the 1st and 16th prime,
      and the number of other primes between them are:
      {320572022166380880, 30, 9, 5, 3}, difference 94, 0 other.
      {87291414128856315, 33, 18, 12, 5}, difference 136, 2 other.
      {57312341532495501, 24, 21, 15, 10}, difference 140, 1 other.
      {82911614607, 45, 15, 7, 3}, difference 140, 1 other.

      The last case was a surprise at only 11 digits.
      It is the only occurrence of that pattern below 10^18.

      --
      Jens Kruse Andersen
    • Mark Underwood
      ... Incredible find! And of course the prime tuple or constellation is symmetrical to boot. ... Hey, some of us rely on surprises that low , hehe. Mark
      Message 2 of 8 , Dec 1, 2008
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        --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
        >
        > I returned to this after completing some other tasks.
        >
        > 320572022166380880 +/- 30 +/- 9 +/- 5 +/- 3 gives 16 distinct
        > consecutive primes. They can also be written:
        > 320572022166380880 +/- n, for n = 13, 19, 23, 29, 31, 37, 41, 47.
        >
        > It is the shared second tightest admissible pattern for
        > 16 distinct primes produced by the additive combinations of
        > 5 numbers where the largest is always added.

        Incredible find! And of course the prime tuple or constellation is symmetrical to boot.


        > The 37 tightest patterns were searched to some limit.
        > 4 of them had a case with 16 primes but only one case had
        > consecutive primes.
        > The 5 numbers, the difference between the 1st and 16th prime,
        > and the number of other primes between them are:
        > {320572022166380880, 30, 9, 5, 3}, difference 94, 0 other.
        > {87291414128856315, 33, 18, 12, 5}, difference 136, 2 other.
        > {57312341532495501, 24, 21, 15, 10}, difference 140, 1 other.
        > {82911614607, 45, 15, 7, 3}, difference 140, 1 other.
        >
        > The last case was a surprise at only 11 digits.
        > It is the only occurrence of that pattern below 10^18.

        Hey, some of us rely on surprises that 'low', hehe.

        Mark
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