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It is known that any prime greater than 2 is odd.

How do I show the combinations of all primes greater than 2 is also odd, $2k+1$?

I tried using induction, but what is appropriate for $prime_n$?

$3 \cdot 5 \cdot 7 \cdot 11 \cdot 2k + 1 = 2k + 1$?

Can we use $2k + 1$ to replace $prime_n$ since we know it will be odd?

Franciele Daltoé
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Noah Deng
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    No, you cannot use $2k + 1$ twice, unless $3\cdot 5 \cdot \ldots = 1$. – pjs36 Dec 03 '15 at 09:07
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    Well, you explicitly have the decomposition of your number into prime factors. And $2$ does not appear there. – lcv Dec 03 '15 at 09:13

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