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