for all
If p and p^2 +2 are primes, then p^3 +2 is a prime.
For this one I assumed that p^3 + 2 is not prime. We can easily note that p(p^2 +2) is not prime. But that's where I've been stuck.
Thanks!
Hi curiousmuch.
It can be shown that is the only prime for which is prime. is not prime whereas is. Any prime is of the form for some integer But is a multiple of 3 and so cannot be a prime
Hence there is only one value of you need to check to see if the statement is true, namely is indeed prime, and so the statement is true.
Sorry. All prime numbers greater than 3 are of the form or , therefore is of the form or . TheAbstractionist said it better. There are no primes of the form , for prime, except for , .
*Is this theorem worded correctly?
EDIT:Haha. "Music of the Primes" by Marcus du Sautoy. Another good one about Erdos is "The Man Who Loved Only Numbers." I've learned more about math from these kinds of books than I ever did getting a math degree in college.Oh thanks, I was confused for a bit. Where did you get that sweet quote by the way?