Results 1 to 6 of 6

Math Help - prime number conjecture

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    62

    prime number conjecture

    disprove the conjecture: There are infinitely many prime numbers expressible in the form n^3 +1 where n is a positive integer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by rmpatel5 View Post
    disprove the conjecture: There are infinitely many prime numbers expressible in the form n^3 +1 where n is a positive integer
    Hint: a^3+b^3 = (a+b)(a^2 - ab + b^2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    62
    I have that part: n^3 +1= (n+1)(n^2-n+1). Just dont know where to go from. I know that 2 is the only integer that will work but i just dont know how to prove it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by rmpatel5 View Post
    I have that part: n^3 +1= (n+1)(n^2-n+1). Just dont know where to go from. I know that 2 is the only integer that will work but i just dont know how to prove it.
    Well because you can factor n^3+1 as a product of two integers.
    So how can it be prime?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2008
    Posts
    62
    so anything that factors can not be prime because that makes it a composite?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by rmpatel5 View Post
    so anything that factors can not be prime because that makes it a composite?
    Yes if a = bc and neither b,c are 1 then a cannot be prime.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: November 19th 2011, 09:10 PM
  2. Replies: 0
    Last Post: September 24th 2011, 11:23 AM
  3. Proof of the Twin Prime Conjecture
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 6th 2010, 10:37 AM
  4. Twin Prime Conjecture - Visual Proof
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 28th 2009, 04:50 AM
  5. Conjecture to establish if a number is not prime
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 18th 2008, 04:48 AM

Search Tags


/mathhelpforum @mathhelpforum