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• ... 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
Message 1 of 37 , Jun 1, 2011
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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
• ... 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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