## Re: Prime 19-tuplet

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• ... Thank you for the extra clarification.
Message 1 of 37 , Jun 3, 2011
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--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
>
> woodhodgson wrote:
> >> The first 25 primes do not make an admissible constellation. It is
> >> impossible to find that pattern repeated anywhere else.
> >
> > That's why I quoted 23, ignoring the "special" first century. There is no
> > reason
> > to rule out the existence of some 23-tuple "inside" a century somewhere.
>
> Right. However, the densest admissible 23-tuples have width 94 but
> cannot be inside a century. They must start with a number which is
> 7 or 9 (mod 10) and then they will cross a multiple of 100.
> But there are admissible 23-tuples with width 96 which can be inside
> a century, for example
> {1,3,7,9,13,21,27,31,37,39,43,49,57,63,67,69,73,79,81,87,91,93,97}
>
> The densest admissible 24-tuples have width 100 so they obviously
> don't fit inside a century.
>
> --
> Jens Kruse Andersen
>

Thank you for the extra clarification.
• ... 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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