Results 1 to 4 of 4

Math Help - Infinite Primes Proof is complete ?

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    2

    Infinite Primes Proof is complete ?

    Hello ,

    The proof to infinite prime numbers is saying that if you create new
    number N from factoring the known finite prime series(P1*P2..*Pn) and
    add 1 ,you will have number that will be new prime ,or be factored
    from new prime that is not included in the finite prime series
    My question is ,how do I prove that the N cannot be factored from
    P1*P1*P2*... which one or more of the primes from the finite series appears more than
    once,the proof is talking only about the case that P1,P2,..Pn appears
    once in the factoring series but what about the option that it appears
    more than once ? .

    Thanks
    Last edited by Eyala; November 2nd 2009 at 02:57 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,528
    Thanks
    1387
    Quote Originally Posted by Eyala View Post
    Hello ,

    The proof to infinite prime numbers is saying that if you create new
    number N from factoring the known finite prime series(P1*P2..*Pn) and
    add 1 ,you will have number that will be new prime ,or be factored
    from new prime that is not included in the finite prime series
    My question is ,how do I prove that the N cannot be factored from
    P1*P1*P2*... which one or more of the primes from the finite series appears more than
    once,the proof is talking only about the case that P1,P2,..Pn appears
    once in the factoring series but what about the option that it appears
    more than once ? .

    Thanks
    What does a prime appearing more than once on the list have to do with anything? The proof does NOT say anything about a "factoring series" (unless you mean the purported "list of all primes" itself) or primes appearing once in a "factoring series". It simply use the fact that either a number is a prime or it is divisible by a prime (which is the definition of "prime" and "composite" numbers). If there were a finite number of primes, P_1, P_2, \cdot\cdot\cdot, P_n, then none of those numbers divides P1*P2*\cdot\cdot\cdot P_n+ 1. Either that number is itself prime or it is divisible by a prime that is NOT on that list. In either case that list does not include all primes.

    If a number has P1*P2 as a factor, then it has P1 as a factor.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    2
    Quote Originally Posted by HallsofIvy View Post
    What does a prime appearing more than once on the list have to do with anything? The proof does NOT say anything about a "factoring series" (unless you mean the purported "list of all primes" itself) or primes appearing once in a "factoring series". It simply use the fact that either a number is a prime or it is divisible by a prime (which is the definition of "prime" and "composite" numbers). If there were a finite number of primes, P_1, P_2, \cdot\cdot\cdot, P_n, then none of those numbers divides P1*P2*\cdot\cdot\cdot P_n+ 1. Either that number is itself prime or it is divisible by a prime that is NOT on that list. In either case that list does not include all primes.

    If a number has P1*P2 as a factor, then it has P1 as a factor.
    The proof relies on the fact that if you divide N by one of the known Primes
    you get 1 as remainder so the prime is not on our finite list,
    but How could you prove that N is not divisable by P1*P1*P2 for example ?
    sometimes numbers are factored by repeated occurance of primes like 4=2*2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Eyala View Post
    The proof relies on the fact that if you divide N by one of the known Primes
    you get 1 as remainder so the prime is not on our finite list,
    but How could you prove that N is not divisable by P1*P1*P2 for example ?
    sometimes numbers are factored by repeated occurance of primes like 4=2*2.

    If the number N is divisible by P1*P1*P2 then it is divisible by P1, something you already showed is impossible

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. infinite primes
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: January 30th 2009, 09:42 AM
  2. infinite primes?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 13th 2007, 04:42 PM
  3. Primes in an Infinite Sequence
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 27th 2007, 12:25 AM
  4. my last question-infinite number of primes
    Posted in the Number Theory Forum
    Replies: 15
    Last Post: December 28th 2006, 10:12 AM
  5. Infinite Primes Proof
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: April 11th 2005, 08:40 AM

Search Tags


/mathhelpforum @mathhelpforum