Results 1 to 5 of 5

Math Help - theorem about primes

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    16

    theorem about primes

    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!
    Last edited by mr fantastic; May 22nd 2009 at 04:10 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    409

    Clarity?

    3| p^2+2 for all p>3
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    Quote Originally Posted by curiousmuch View Post
    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 p=3 is the only prime for which p^2+2 is prime. 2^2+2=6 is not prime whereas 3^2+2=11 is. Any prime p\ge5 is of the form 6n\pm1 for some integer n. But (6n\pm1)^2+2=36n^2\pm12n+3 is a multiple of 3 and so cannot be a prime \ge5.

    Hence there is only one value of p you need to check to see if the statement is true, namely p=3. 3^3+2=29 is indeed prime, and so the statement is true.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    16
    Quote Originally Posted by Media_Man View Post
    3| p^2+2 for all p>3
    Oh thanks, I was confused for a bit. Where did you get that sweet quote by the way?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    409
    Sorry. All prime numbers greater than 3 are of the form 6n+1 or 6n+5, therefore p^2+2 is of the form 36n+12n+1+2=3(12n+4n+1) or 36n+12n+25+2=3(12n+4n+9) . TheAbstractionist said it better. There are no primes of the form p^2+2, for p prime, except for p=3, p^2+2=11.

    *Is this theorem worded correctly?

    EDIT:
    Oh thanks, I was confused for a bit. Where did you get that sweet quote by the way?
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. primes?
    Posted in the Number Theory Forum
    Replies: 9
    Last Post: January 13th 2010, 07:37 PM
  2. About Primes
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: August 17th 2009, 06:44 AM
  3. Primes help
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: May 12th 2009, 09:01 PM
  4. Help with primes
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: January 20th 2009, 09:01 PM
  5. Euclid's theorem and primes numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 10th 2006, 08:33 AM

Search Tags


/mathhelpforum @mathhelpforum