If p, q > 2 are consecutive in set of primes. Since p,q can only be odd number, (p+q) is an even number.

Can (p+q)/2 be prime?

from http://republicofmath.com/

NO

"There are no primes between p & q..." from @JoeUchill

I think this question is awesome because it reminded me at the first glance that “there are arbitrarily long arithmetic progressions of primes” proven by Green and Tao. http://arxiv.org/abs/math.NT/0404188

So it appeared as a tough question and I immediately gave up...

## Comments

Sign uporlog in with Facebookto comment.SurajdubeyNo..!!

RaviThere's a

Show Answerbutton below the puzzle!AakashTook me longer than I'd like to admit...very nice though.

pratik31no

flowerkingYes.. took some of thinking to figure out , but Good one!

Kranthi KrishnaCounterexample: 11, 13 are consecutive primes. 12 is not. So the answer is NO.

Виктория ЯцковаNever. Otherwise the would be a prime number between p and q.