--- "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.