rupert.wood wrote:

> 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).

I used my own unpublished prime pattern finder. It is modified for

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?

> For instance 9100524636850+n is also prime for n=21

I listed this and the primes for the other cases in my first post

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

>

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

5431, 5437 and 5483 are also prime.

--

Jens Kruse Andersen