SOLUTION: I need some help with a proof. 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. Exam

SOLUTION: I need some help with a proof. 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. Exam

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Question 275854: I need some help with a proof.
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.
Examples: 11, 13 11+13=24 13,17 13+17=30
Thank you
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

All you need to do to prove that it is NOT true is to find a counter-example.

2 plus 3 = 5. 5 is prime.

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

.

Then

which is clearly an even, and therefore composite, number.

John

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