Thread: Adding a certain amount of primes

I don't really know where this question belongs but I will ask it here.

Its kind of a weird question. It has to do with a way I came up to solve a computer algorithm.

Say I have a set of primes A={ 0,3,5,7} (can't include 1)

And say I must sum n numbers where all of the numbers must be from the set A.

Will there only be one possible way to get any result.

Say n = 6

That means I must sum 6 numbers x1+x2+x3+x4+x5+x6=Y where any xi must be from the set A. Is there more than one way the get the same result for y, not counting repeating patterns when it always must be 6 numbers selected?

Like when i just add it out on a small scale it seems like the answer is that there is only one unique way.

Say 3+3+5+7+0+7=25

So now can I get an answer of 25 when summing a different combination of the values 0,3,5,7 of length 6?

Could you do it if it was very big?

When you add 1 it does not hold at all.

Since

7+7+7+1+3=25

If it does hold for the numbers 0,3,5,7 does it hold for all relatively prime numbers?

Originally Posted by ehpoc

I don't really know where this question belongs but I will ask it here.

Its kind of a weird question. It has to do with a way I came up to solve a computer algorithm.

Say I have a set of primes A={ 0,3,5,7} (can't include 1)

And say I must sum n numbers where all of the numbers must be from the set A.

Will there only be one possible way to get any result.

Say n = 6

That means I must sum 6 numbers x1+x2+x3+x4+x5+x6=Y where any xi must be from the set A. Is there more than one way the get the same result for y, not counting repeating patterns when it always must be 6 numbers selected?

Like when i just add it out on a small scale it seems like the answer is that there is only one unique way.

Say 3+3+5+7+0+7=25

So now can I get an answer of 25 when summing a different combination of the values 0,3,5,7 of length 6?

Could you do it if it was very big?

When you add 1 it does not hold at all.

Since

7+7+7+1+3=25

If it does hold for the numbers 0,3,5,7 does it hold for all relatively prime numbers?

Neither 0 or 1 are primes.

CB

Ya I wasn't thinking there but I should say primes and 0.

But either way still can get what I mean though.

"Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:
Every even integer greater than 2 can be expressed as the sum of two primes." (wikipedia)

Goldbach's conjecture - Wikipedia, the free encyclopedia

Assuming that the conjecture is true then any odd number greater than 5 can be expressed as the sum of three primes (just subtract 3 from t any you have an even number greater than 2).


Specifically 2 and 23 are both primes:
0 + 0 + 0 + 0 + 2 + 23 = 25
0 + 0 + 0 + 3 + 5 + 17 = 25
0 + 0 + 0 + 3 + 11 + 11 = 25
0 + 0 + 0 + 5 + 7 + 13 = 25
0 + 3 + 3 + 3 + 3 + 13 = 25
0 + 5 + 5 + 5 + 5 + 5 = 25
etc.