Prove that if both p and p^2 + 8 are prime numbers, then p^3 + 10 is also prime

thanks.

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- Sep 24th 2009, 02:15 PMciccioPrime numbers
Prove that if both p and p^2 + 8 are prime numbers, then p^3 + 10 is also prime

thanks. - Sep 24th 2009, 04:42 PMPaulRS
If , then which is again prime, and surely enough is prime.

Now if - and p prime-, then -since p must be coprime to 3- thus so cannot be prime now.

Then, since and are primes simultaneously only for , and in this case the assertion is true, we are done.