Loading ...
Sorry, an error occurred while loading the content.

"problem" with Euclid's proof of the Infinitude of Primes

Expand Messages
  • duke nukem
    I am having a problem with Euclid s proof of the Infinitude of Primes. Sorry for the not so short post ahead :) Please see this link for the modern
    Message 1 of 1 , Jan 31, 2004
      I am having a "problem" with Euclid's proof of the Infinitude of Primes.

      Sorry for the 'not so short post' ahead :)

      Please see this link for the modern translation of the proof (note there are 2 versions there, don't forget the one in the bottom of the page :).
      These versions are considered true (of course) and can be found in most textbooks.
      the link:

      Now the "problem" is that I came across this "ShortCut Version" of proof which looks like a real shortcut to Euclid's proof.
      I am wondering if there is any mistake/hidden assumption/etc. I am missing here:
      The proof gos like that:
      (1). The prime numbers are the numbers p1,p2,...,pn,... of set S.
      Suppose S is finite [supposition].

      (2). If S is finite then: p1,p2,...,pn is the complete series set, so that pn is the largest prime.

      (3). Form W+1 = (p1xp2x,...,xpn) + 1.
      W+1 is not in the set S so it is not prime.
      W+1 is not divisible by any of primes in S_P so it
      is prime.
      Reverse supposition and primes are infinite.

      I do not think the 'counter example': 2*3*5*7*11*13+1= 30031 = 59*509 => hence a composite W+1, work here.
      because 2,3,5,7,11,13 isn't the Actual list of All primes. its a partial list and for that reason doesn't necessarily has the same attribute as the complete list.
      To me this looks the same as this:
      say 1,2,3,4,5 are all the "favorite" numbers.
      ["favorite" - a set I just made up].
      My Great Theorem: the sum of all "favorite" numbers is odd.
      proof: 1+2+3+4+5=15. QED :)
      Now one would say: "but look - 1+2+3=6" so there is a partial sum that is Even.
      And I would answer: but my theorem is about the sum of ALL the favorite numbers, so we are talking about different cases!.
      * would I be correct? If not, why?

      Thanks for your kind insights,
      Please ignore all Ads below this line.

      Get advanced SPAM filtering on Webmail or POP Mail ... Get Lycos Mail!
    Your message has been successfully submitted and would be delivered to recipients shortly.