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Sum of Two Prime Numbers 10

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/

"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...

Surajdubey

No..!!

Ravi

There's a Show Answer button below the puzzle!

Aakash

Took me longer than I'd like to admit...very nice though.

pratik31

no

flowerking

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

Kranthi Krishna

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

Виктория Яцкова

Never. Otherwise the would be a prime number between p and q.

leilei3915

2018529 leilei3915

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