How to begin to solve this problem? http://www.mymathforum.com/images/smilies/icon_wink.gifQuote:

Find all primes $\displaystyle p$ such that the number of $\displaystyle (p^6)+6$ is also a prime number.

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- Nov 4th 2012, 04:22 PMmakramerPrime numbersQuote:

Find all primes $\displaystyle p$ such that the number of $\displaystyle (p^6)+6$ is also a prime number.

- Nov 4th 2012, 05:02 PMPetekRe: Prime numbers
The way I solved this problem was to use Wolfram Alpha: Plug in expressions of the form

*Factor p^6 + 6*

where p = 2, 3, 5, 7, 11, 13, 17, 19 and so on until you see a pattern. Then use what you know (perhaps Fermat's Little Theorem) to prove your guess. Others might be able to see the solution more quickly, but that's how I did it. - Nov 4th 2012, 06:36 PMrichard1234Re: Prime numbers
Hint: Consider $\displaystyle p^6 + 6$ modulo some other prime q. Without much computation, I was able to find a q such that $\displaystyle p^6 + 6 \equiv 0 (\mod q)$ for all p.