[PrimeNumbers] Re: The evolution of a tuple
- Mark Underwood wrote:
> There are exactly 168 primes from 1 to 1,000. IThe smallest admissable 168-tuplet is 1033 wide according to an exhaustive
> wouldn't be surprised at all now if a prime constellation waaaay up
> there somewhere exeeds 168 primes in an interval of 1,000.
search by Thomas J. Engelsma:
His current results say that if there is a prime tuplet closer together than the
earliest primes then it must be at least a 311-tuplet.
From inexhaustive searching, his smallest admissable tuplet beating the earliest
primes is a 447-tuplet of width 3159, where p(447) = 3163. Finding an occurrence
of such a tuplet is out of the question today. However I agree with the k-tuplet
conjecture that there are infinitely many.
Jens Kruse Andersen