document.write( "Question 275854: I need some help with a proof.
\n" ); document.write( "Let p & q be 2 consecutive primes. Then p+q=2n for some n. Is n always composite. I have some examples but not sure how to write proof.\r
\n" ); document.write( "\n" ); document.write( "Examples: 11, 13 11+13=24 13,17 13+17=30\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #201143 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "All you need to do to prove that it is NOT true is to find a counter-example.\r
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\n" ); document.write( "\n" ); document.write( "2 plus 3 = 5. 5 is prime.\r
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\n" ); document.write( "\n" ); document.write( "On the other hand, if you exclude 2 by saying p and q are 2 consecutive odd primes, then the theorem is true. Except for 2, all primes are odd and of the form

. So we can say that

and

for some

and

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\n" ); document.write( "\n" ); document.write( "Then

which is clearly an even, and therefore composite, number.\r
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\n" ); document.write( "\n" ); document.write( "John
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