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

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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
Message 1 of 8 , Dec 1, 2008
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
• ... 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
--- 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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