- 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

--- In primenumbers@yahoogroups.com, "Mark Underwood"

<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.

> - Mark Underwood wrote:

> And for the tuple

I have computed the 4 smallest x such that these 14 are all primes:

>

> 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.

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 - I wrote:
> x +/- 2, 4, 8, 16, 32, 64, 128

A Google search on 93487500801880185 reveals that it was first found by Jim:

> x = 93487500801880185.

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