## Re: distance between prime tuples

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• Some trivia: As it turns out, for a tuple of the form x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32 x must indeed have a factor of 3,5,7 and 11 And for
Message 1 of 7 , Jun 1, 2005
Some trivia:

As it turns out, for a tuple of the form

x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32

x must indeed have a factor of 3,5,7 and 11

And for the tuple

x-64, x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32, x+64

x must have a factor of 3,5,7,11,13.

However, breaking the trend, the 16 term tuple doesn't require that x
has a factor of 17, only 3,5,7 and 11. But the 18 term tuple does
require x to have a factor of 19 (as well as 3,5,7,11,and 13).

Mark

<mark.underwood@s...> wrote:
>
> I just took a look and find that a tuple of the form
> x-8, x-4, x-2, x+2, x+4, x+8
> must have x = 3*5*7*k.
>
> Extrapolating, perhaps a tentuple of the form
> x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32
> must have x = 3*5*7*11*k. I'll soon see.
>
• ... I have computed the 4 smallest x such that these 14 are all primes: x +/- 2, 4, 8, 16, 32, 64, 128 A PrimeForm/GW input file with x values in {. . . .} :
Message 2 of 7 , Jun 1, 2005
Mark Underwood wrote:

> And for the tuple
>
> x-64, x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32, x+64
>
> x must have a factor of 3,5,7,11,13.

I have computed the 4 smallest x such that these 14 are all primes:
x +/- 2, 4, 8, 16, 32, 64, 128

A PrimeForm/GW input file with x values in {. . . .} :

ABC2 \$b+2^\$a & \$b-2^\$a
a: from 1 to 7
b: in {93487500801880185 539493168332973855 635219113875010665
892427005980104595}

My tuplet finder used 5 GHz hours with prp'ing by the GMP library.
I was surprised to see that the primes are consecutive for the smallest,
x = 93487500801880185.

--
Jens Kruse Andersen
• ... A Google search on 93487500801880185 reveals that it was first found by Jim: http://www.primepuzzles.net/puzzles/puzz_167.htm Phil then found
Message 3 of 7 , Jun 1, 2005
I wrote:
> x +/- 2, 4, 8, 16, 32, 64, 128
> x = 93487500801880185.

A Google search on 93487500801880185 reveals that it was first found by Jim:
http://www.primepuzzles.net/puzzles/puzz_167.htm

Phil then found 64606701602327559675 +/- 2, 4, 8, 16, 32, 64, 128, 256

So I'm 3 years late and didn't even rediscover the best result :-(
Extending to +/- 512 is too hard for me.

--
Jens Kruse Andersen
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