## 18004Re: additive combinations all prime?

Expand Messages
• May 7, 2006
• 0 Attachment
--- "Mark Underwood" <mark.underwood@...> wrote:
>
> 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!
> Mark
----------------------------------------------------------------------

Something interesting with the product of the numbers ?

(1,4)--> 4 = 2^2
(1,4,8)--> 32 = 2^5
(3,5,8,13)--> 1560 = 2^3 * 3 * 5 * 13
(3,10,12,15,27)--> 145800 = 2^3 * 3^6 * 5^2
(5,30,33,42,60,63)--> 785862000 = 2^4 * 3^6 * 5^3 * 7^2 * 11

In each case the product of the n numbers gives a number whose number
of different prime factors (in the factorization) is smaller or equal
to n.
Is it always the case ?

Patrick Capelle.
• Show all 10 messages in this topic