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
    10
    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
    10
    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
    10
    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, 10:10 PM
  2. Replies: 0
    Last Post: September 24th 2011, 12:23 PM
  3. Proof of the Twin Prime Conjecture
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 6th 2010, 11:37 AM
  4. Twin Prime Conjecture - Visual Proof
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 28th 2009, 05:50 AM
  5. Conjecture to establish if a number is not prime
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 18th 2008, 05:48 AM

Search Tags


/mathhelpforum @mathhelpforum