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

Algebra ->  Divisibility and Prime Numbers -> 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      Log On


   

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) About Me  (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