- woodhodgson wrote:
> Centuries refer to ranges [100X+1,100X+99]. Does anyone happen to know

There is no case of consecutive centuries with more than 5 primes below 10^12.

> where the first repetition of the primes in a century occurs? I see no reason to

> suspect that this would necessarily happen to be from the first 2 void centuries.

> A very minor point in the prime universe perhaps, but one I have long wondered about.

The following assumes that non-consecutive centuries are allowed.

The first case measured by the larger century:

{390500, 480800} + {3, 27, 39, 53, 81}

The first case measured by the average:

{78900, 578700} + {1, 19, 29, 41, 77, 79, 89}

The first repetition of the first century with less than 16 primes

(meaning I could quickly find a repetition):

{500, 47843760324362600} + {3, 9, 21, 23, 41, 47, 57, 63, 69, 71, 77, 87, 93, 99}

--

Jens Kruse Andersen --- 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