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If p and q are prime numbers, where p is no more than q, is sum of p and q a prime number? (1) p is not equal to q. (2) p is greater than 2.

If p and q are prime numbers, where p is no more than q, is sum of p and q a prime number?

The sum of two primes to be a prime number necessary but not sufficient condition is one of the primes to be 2 and another more than 2 (so that the sum to be odd and have a chance to be a prime number), for example: 2+3=5 or 2+5=7 or 2+11=13. If both primes are more than 2 then both will be odd primes and their sum will be even>2, so not a prime number

(1) p is not equal to q --> if p=2 and q=3 then the answer will be YES but if p=2 and q=7 then the answer will be NO. Not sufficient.

(2) p is greater than 2 --> \(2<p\) as also given that \(p\leq{q}\) then \(2<p\leq{q}\) thus both primes are more than 2 --> their sum is even so not a prime number. Sufficient.

Re: If p and q are prime numbers, where p is no more than q, [#permalink]

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10 Feb 2011, 16:41

oh, I see... Two odd prime no will always sum up to be an even no cause O+O=E.And statement two proves that both p and q are Odd primes.Thank you Bunuel for the explanation.

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Re: If p and q are prime numbers, where p is no more than q, is [#permalink]

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09 Sep 2013, 04:45

monirjewel wrote:

"p is no more than q". Does it mean p=q?

It is a little non-restrictive than that.It means \(p\leq{q}\). So the max p can be IS q, but not more than that. But, it can be less than q.
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Re: If p and q are prime numbers, where p is no more than q, is [#permalink]

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19 Jun 2016, 02:16

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