19234Re: additive combinations all prime?
- Feb 5, 2008--- In email@example.com, "Mark Underwood"
>Took a nice sabbatical from numbers, namely the primes. The things
> Well surprise of surprises:
> The six numbers (5,30,33,42,60,63) yield primes for all 32 additive
> combinations of the six numbers.(!) I thought it would have been
> waaay higher.
> So we have as first cases:
> (1,4) has all 2 additive combinations yielding 2 primes.
> (1,4,8) has all 4 additive combos yielding 4 primes.
> (3,5,8,13) has all 8 additive combos yielding 8 primes.
> (3,10,12,15,27) has all 16 additive combos yielding 16 primes.
> (5,30,33,42,60,63) has all 32 additive combos yielding 32 primes.
> Interesting that thus far the greatest number in each set does not
> quite exceed 2^n. Surely that can't hold up for long...or can it?
> Wonders never cease!
drive me crazy. But in a momement of weakness/boredom, perhaps abit of
seasonal affective disorder, I looked back over some of my
Very shortly after this post from about a year and a half ago, I found
a way to greatly speed up the search for additive combinations which
yeild all primes. For instance: for six numbers, each not exceeding
500, I found on the order of about 70 different solutions, each
yeilding (in their 32 additive combinations) all primes. But I noted
only one which yielded 32 *distinct* primes:
in its 32 additive combinations yields the 32 unique primes
I tried a similar technique to get 7 numbers with all 64 additive
combinations yielding only primes, but with no success. I don't think
there is a solution if all the numbers are below 1000, but it wasn't
quite an exhaustive search.
Just throwing this out in case anyone is interested, before I entirely
forgot about it.
- << Previous post in topic Next post in topic >>