## Pairing up consecutive numbers may give a prime..(Self-made)

For discussing Olympiad Level Number Theory problems
Fm Jakaria
Posts: 77
Joined: Thu Feb 28, 2013 11:49 pm

### Pairing up consecutive numbers may give a prime..(Self-made)

Is it true that for each even positive integer $n$, the integers $1$ through $n$ can be paired with each other into $\frac{n}{2}$ pairs - so that the product of each pairs, when summed up - gives a prime number?

For example, for $n = 8$, we can pair up $1,7$; $2,8$; $3,6$; $4,5$. Then $1*7+ 2*8+ 3*6+ 4*5$ equals $61$, a prime.....

If this isn't true, find the least counterexample $n$.
I do mathematics, but still I have no evidence that absence of evidence is not evidence of absence.