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RE: [PrimeNumbers] Finitude of primes

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  • chriscard1@netscape.net
    ... Even primes? Chris __________________________________________________________________ McAfee VirusScan Online from the Netscape Network. Comprehensive
    Message 1 of 14 , Oct 1, 2003
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      "mad37wriggle" <fitzhughrichard@...> wrote:

      >
      >Are there any types/forms of primes of which there are definitely
      >only a finite number? I'm sure there must be, but can't think of
      >any off the top of my head. I'd be interested to see the proofs of
      >finitude...
      >
      Even primes?


      Chris

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    • Chris Caldwell
      ... Even primes... Primes divisible by three... Primes of the form x^2-1 (or x^n-1)...
      Message 2 of 14 , Oct 1, 2003
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        At 01:33 PM 10/1/2003 +0000, mad37wriggle wrote:

        >Are there any types/forms of primes of which there are definitely
        >only a finite number? I'm sure there must be, but can't think of
        >any off the top of my head. I'd be interested to see the proofs of
        >finitude...

        Even primes...
        Primes divisible by three...
        Primes of the form x^2-1 (or x^n-1)...
      • mad37wriggle
        OK let me attempt to rephrase that so as to avoid trivial solutions... Are there any types/forms of primes of which there are definitely only a finite ( 1
        Message 3 of 14 , Oct 1, 2003
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          OK let me attempt to rephrase that so as to avoid "trivial"
          solutions...

          Are there any types/forms of primes of which there are definitely
          only a finite (>1 and taken over all possible primes so that
          "primes less then N" or "primes with k digits" etc. are not
          permissible) number?

          Richard



          --- In primenumbers@yahoogroups.com, chriscard1@n... wrote:
          > "mad37wriggle" <fitzhughrichard@h...> wrote:
          >
          > >
          > >Are there any types/forms of primes of which there are
          definitely
          > >only a finite number? I'm sure there must be, but can't think of
          > >any off the top of my head. I'd be interested to see the proofs
          of
          > >finitude...
          > >
          > Even primes?
          >
          >
          > Chris
          >
          >
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        • Gary Chaffey
          Fermat Primes are only finite in number. I think I would be right in saying there are infinitely many types of primes which yield only a finite number of
          Message 4 of 14 , Oct 1, 2003
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            Fermat Primes are only finite in number.
            I think I would be right in saying there are
            infinitely many 'types' of primes which yield only a
            finite number of primes
            Gary

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          • Paul Jobling
            ... The heuristics certainly say that, but has it been definitely proven? __________________________________________________ Virus checked by MessageLabs Virus
            Message 5 of 14 , Oct 1, 2003
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              > Fermat Primes are only finite in number.

              The heuristics certainly say that, but has it been definitely proven?

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            • jbrennen
              ... Still, that restriction allows trivial solutions. I came up with this one in just a few minutes, and there are an infinite number of examples like this:
              Message 6 of 14 , Oct 1, 2003
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                --- "mad37wriggle" wrote:
                >
                > OK let me attempt to rephrase that so as to avoid "trivial"
                > solutions...
                >
                > Are there any types/forms of primes of which there are definitely
                > only a finite (>1 and taken over all possible primes so that
                > "primes less then N" or "primes with k digits" etc. are not
                > permissible) number?

                Still, that restriction allows "trivial" solutions. I came up
                with this one in just a few minutes, and there are an infinite
                number of examples like this:


                There are exactly two primes which are of the form:

                4*x^2 - 31*x + 60, with x an integer
              • Andy Swallow
                ... Not true. The number of Fermat primes is suspected to be finite, but it has not been proved. As far as I know, anyway. Unless my books are out of date!
                Message 7 of 14 , Oct 1, 2003
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                  > Fermat Primes are only finite in number.

                  Not true.
                  The number of Fermat primes is suspected to be finite, but it has not
                  been proved. As far as I know, anyway. Unless my books are out of date!

                  Andy
                • mikeoakes2@aol.com
                  In a message dated 01/10/03 15:25:15 GMT Daylight Time, caldwell@utm.edu ... Not the second of these: restrict to x = 2 and you have made a probably-false
                  Message 8 of 14 , Oct 1, 2003
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                    In a message dated 01/10/03 15:25:15 GMT Daylight Time, caldwell@...
                    writes:


                    > Primes of the form x^2-1 (or x^n-1)...
                    >
                    Not the second of these: restrict to x = 2 and you have made a probably-false
                    statement:-)

                    Mike



                    [Non-text portions of this message have been removed]
                  • Gary Chaffey
                    In an earlier mail I stated:- Fermat Primes are only finite in number. I think I should of worded this more carefully . I know that this is only a conjecture
                    Message 9 of 14 , Oct 1, 2003
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                      In an earlier mail I stated:-
                      Fermat Primes are only finite in number.
                      I think I should of worded this 'more carefully'. I
                      know that this is only a conjecture but it is another
                      one of those conjectures which although hasn't been
                      proven most evidence points this way.



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                    • Gary Chaffey
                      Fermat Primes are only finite in number. P.S. I do have a proof for this but it will not fit in the margin!!!
                      Message 10 of 14 , Oct 1, 2003
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                        Fermat Primes are only finite in number.
                        P.S.
                        I do have a proof for this but it will not fit in the
                        margin!!!




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                      • Paul Jobling
                        On this subject, is there any set of primes that has been shown to have a finite - but unknown - number of elements? I can t think of any, though there are
                        Message 11 of 14 , Oct 1, 2003
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                          On this subject, is there any set of primes that has been shown to have a
                          finite - but unknown - number of elements? I can't think of any, though there
                          are many which are heuristically thought to be finite (such as the Fermat
                          primes).

                          - Paul.


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