## Re: [PrimeNumbers] A prime 15-tuplet

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• ... Fantastic effort. As someone with more than a passing interest in both small-prime big-combination results and hacking together my own code that gets the
Message 1 of 3 , Oct 30, 2001
On Mon, 29 October 2001, "Hadley, Thomas H (Tom), NLCIO" wrote:
> I'd like to announce the discovery of a prime 15-tuplet. This set of 15
> primes matches the set (11,13,17,19,23,29,31,37,41,43,47,53,59,61,67) which
> contains all the primes between 11 and 67. This is the maximum length
> possible for this pattern. (If 71 is put in the list, then one of the
> numbers will be divisible by 11).
>
> year ago and decided I would try to find an example. This gave me a goal to
> work towards as I developed a C++ large-integer package of my own. I got
> some good input on algorithms from Jim Morton of the list, and put my little
> pentium 233 to work.

Fantastic effort. As someone with more than a passing interest in both small-prime big-combination results and hacking together my own code that gets the job done (and also running code on 'legacy' machines like P133s and PPro200s) I can't emphasise my congratulations strongly enough. I considered attacking this very problem last week as I was reading Riesel while on holiday (sad, sad man :-) ).

> I finally found a solution after many, many months of searching!! As
> someone else on the list said recently, "Yippee!!"
>
> The numbers are:
>
> 44360646117391789301 + (0,2,6,8,12,18,20,26,30,32,36,42,48,50,56)
> (20 digits)

That's larget than expected, I believe (which gave me confidence in the fact that (if I were to only get off my lazy bum and fix my 'gensv' code) I could find one myself).

> I submitted the number to Tony Forbes and he put it on his list of "smallest
> 15-tuplets". Someone else had already found two examples, but one of these
> had 21 digits, the other 30 digits!! And unless I have a bug in my
> software, mine is the smallest constellation with this exact pattern (except
> of course, 11,13,17,...,67).

I took a 'sickie' yesterday, and worked on my 'gensv' (Paul - it has a couple of real bugs which will cause it to reject numbers incorrectly. Luis - yes, I can look at Euler trinomials again, mail me), and at about 3am (gotta love that Finnish coffee!) decided that it was close enough to working to be able to remove debug info and run it on your problem. I reckon that I can use your result to help verify my code, as I hope to reproduce the result using independent code to give you increased confidence in your code. (I'm sure it's less buggy than mine!)

I don't know if you recorded any 'near misses', which would help me check that I'm on track? If so, could I have a copy please.
For example, I discovered a near-miss 13-tuple (+50/+56 missing) at 2,365,201,889,521,345,991 overnight (and 2 12-tuples missing 48 too before then).

> some time this
> I recommend Tony's site for anyone interested in prime k-tuples. It is at:
>
> http://www.ltkz.demon.co.uk/ktuplets.htm
>
> Thank you to everyone on the list for all I've learned.

The list's like that a lot of the time, isn't it!

Well done again,

Phil

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