- Does it not matter that primes exist between them? For instance 9100524636850+n is also prime for n=21

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com, "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I used my own unpublished prime pattern finder.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

http://tech.groups.yahoo.com/group/primenumbers/message/21242

The original post said prime quadruplets are permitted and also listed:

> There is an instance of 4 consecutive triplets at

5431, 5437 and 5483 are also prime.

>

> 5413 5417 5419; 5441 5443 5449; 5471 5477 5479; 5501 5503 5507.

--

Jens Kruse Andersen