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

For discussing Olympiad Level Number Theory problems
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Fm Jakaria
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Pairing up consecutive numbers may give a prime..(Self-made)

Unread post by Fm Jakaria » Sat Jul 08, 2017 10:45 pm

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.

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samiul_samin
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Re: Pairing up consecutive numbers may give a prime..(Self-m

Unread post by samiul_samin » Sat Dec 09, 2017 2:20 pm

Can you give any hint to find the least counterexample n?

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