Question

another small challenge for those who are bored:

Give that p and q are consecutive primes, show that the equation p + q = 2r, where r
is prime, has no solutions.

Answer 1

this is not that hard, any ideas?

Answer 2

Well, we now p or q is not 2.

Answer 3

sorry --- know -- keys are sticky, ewwwww....

Answer 4

:)

Answer 5

Should we write p = 2k+1, for some integer k,
and q = 2j + 1 for some integer j

Answer 6

rearranging give r=(p+q)/2

(p+q)/2 what is this?

Answer 7

average

Answer 8

But p and q are consecutive primes :)

Answer 9

yep, that is it!

Answer 10

oh lol
good one :)

Answer 11

I found quite a few smaller challenges, there are a few fun ones

Answer 12

I would like to see them, they are quite interesting

Answer 13

I will post a new one now