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# Can teh positive integer n be written as the sum of two

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Can teh positive integer n be written as the sum of two [#permalink]  31 Mar 2008, 10:08
Can teh positive integer n be written as the sum of two different positive prime numbers?

1) n is greater than 3
2) n is odd

many thanks
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Re: positive integer [#permalink]  31 Mar 2008, 10:14
primes: 1,3,5,7,11,13,17,etc

sum of any two primes is even.

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Re: positive integer [#permalink]  02 Apr 2008, 07:33
onyxls1 wrote:

sum of any two primes is even.

5 = 2 + 3 (2 & 3 are prime but 5 is not even)
7 = 2 + 5 (2 & 5 are prime but 7 is not even)
9 = 2 + 7 (2 & 7 are prime but 9 is not even)
13 = 2 + 11 (2 & 11 are prime but 13 is not even)
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Re: positive integer [#permalink]  02 Apr 2008, 07:37
I will go with E..

pick 23..23 cannot be expressed as the sum of 2 different primes

13 can be expressed as 11+2
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Re: positive integer [#permalink]  02 Apr 2008, 07:45
Expert's post
E

1. Let n satisfies both conditions
2. n can be odd only if one of the prime numbers is 2.
3. Therefore, n=p+2
4. p can be prime number (5,7,11,13,17) and can be not prime number (9,15)
5. Therefore, E

we now can also construct two examples:
5=3+2 and 11=9+2
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Re: positive integer [#permalink]  02 Apr 2008, 07:54
puma wrote:
Can teh positive integer n be written as the sum of two different positive prime numbers?

1) n is greater than 3
2) n is odd

many thanks

E.

Personally I don't like the wording of this DS question. It can be confusing.

The question is asking can it be the sum of two positve prime numbers. Well really we can answer Yes it can be. It should read "IS n the sum of two different positive prime numbers." Just my opionion there.

Anyway when you get these, follow the same rules that apply to all yes and no questions.
Re: positive integer   [#permalink] 02 Apr 2008, 07:54
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