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• ## Re: [PrimeNumbers] First repetition of prime pattern within "centuries"

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• ... [SNIP - me showing the mental faculties of your average seafood] ... Again, extreme short-sightedness, I just presumed they d be in numerical order. I m
Message 1 of 11 , May 16, 2011
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--- On Mon, 5/16/11, Jens Kruse Andersen <jens.k.a@...> wrote:
[SNIP - me showing the mental faculties of your average seafood]
> The century starting at 0 is obviously inadmissible. The
> century starting
> at 100 is the first admissible but it has 21 primes and
> that would be
> computationally extremely hard to repeat although the
> k-tuple
> conjecture predicts infinitely many cases.
>
> >> First case with 0 to 5 primes in the century:
> >> 0: {47326700, 47326800} + {}
> >> 1: {180882800, 180882900} + {17}
>
> > Why doesn't {72676000, 72676100} + {33, 57, 69, 81} appear
> > between those two? And {177343900, 177344000} + {9, 39, 93} also?
>
> My post continued:
> >> 2: {251848800, 251848900} + {1, 43}
> >> 3: {177343900, 177344000} + {9, 39, 93}
> >> 4: {72676000, 72676100} + {33, 57, 69, 81}
> >> 5: {3451361900, 3451362000} + {11, 17, 23, 59, 71}
>
> It was sorted by the number of primes "0 to 5" and gave the
> first case with that number of primes.

Again, extreme short-sightedness, I just presumed they'd be in numerical order.

I'm pretty sure I confused the "send" and "cancel" buttons, as I'm sure I had shed most my confusion at some point, and thus my silly questions were unnecessary.

It appears you've only attacked this from an angle of finding the easiest pattern to detect, rather than an exhaustive one. As primes tend towards sparseness, this is clearly the optimal approach. However, with that view-point, the denser patterns are the more interesting ones - I wonder what remains yet undiscovered?

Sorry for being dense. In my defence, the score was 6-1, so it was a very long night.
Phil
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