Re: Consecutive occurrences of decadal prime triplets
- --- In firstname.lastname@example.org, "Jens Kruse Andersen" <jens.k.a@...> wrote:
>Thanks for that!
> I wrote:
> > 9100524636850 + n, for n =
> > 1, 7, 9, 31, 33, 37, 61, 63, 69, 91, 93, 99, 121, 127, 129.
> > 283955584598830 + n, for n =
> > 1, 7, 9, 33, 37, 39, 61, 63, 69, 91, 93, 97, 121, 123, 127.
> > 488187768695650 + n, for n =
> > 1, 7, 9, 31, 37, 39, 63, 67, 69, 93, 97, 99, 121, 127, 129.
> My search says these are the first three instances of 5 triplets.
> I don't have resources to search for 6 triplets.
> Jens Kruse Andersen
Just to avoid unnecessary effort and extra computer time, are there any coding shortcuts for this kind of searching? Even in the 4-triplet case there would be quite a bit of tedious checking to do in each iteration (just asking in case someone has developed some generic sort of prime pattern searching routine).
- rupert.wood wrote:
> Just to avoid unnecessary effort and extra computer time,I used my own unpublished prime pattern finder. It is modified for
> are there any coding shortcuts for this kind of searching?
> Even in the 4-triplet case there would be quite a bit of
> tedious checking to do in each iteration (just asking in
> case someone has developed some generic sort of prime
> pattern searching routine).
each search and not suited for sharing. It could probably easily
find thousands of 4-triplet cases if it was modified for the purpose.
There are many possible shortcuts evolving around avoiding or quickly
eliminating cases where at least one number has a small prime factor.
I searched each of the 194 admissible 5-triplet patterns one at a time,
so in each case there were 15 numbers that had to be prime. Searching
some patterns with few differences at the same time might be more
efficient but I didn't have suitable code for that.
A shortcut you may already use is to only make prp (probable prime)
tests at first, and only make primality proofs later when there is a
complete prp solution.
Using fast tools like C instead of PARI/GP can also speed up many things.
Robin Garcia wrote:
> Does it not matter that primes exist between them?I listed this and the primes for the other cases in my first post
> For instance 9100524636850+n is also prime for n=21
The original post said prime quadruplets are permitted and also listed:
> There is an instance of 4 consecutive triplets at5431, 5437 and 5483 are also prime.
> 5413 5417 5419; 5441 5443 5449; 5471 5477 5479; 5501 5503 5507.
Jens Kruse Andersen