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Re: [PrimeNumbers] Finitude of primes

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  • mikeoakes2@aol.com
    In a message dated 01/10/03 14:35:10 GMT Daylight Time, ... = 0 mod 2. (Proof left as an exercise|-) Mike [Non-text portions of this message have been removed]
    Message 1 of 14 , Oct 1, 2003
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      In a message dated 01/10/03 14:35:10 GMT Daylight Time,
      fitzhughrichard@... writes:


      > 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...

      = 0 mod 2.
      (Proof left as an exercise|-)

      Mike


      [Non-text portions of this message have been removed]
    • richyfourtythree
      How abot one-digit-primes? ;-) Well there surely are more interesting ones ... richyfourtythree
      Message 2 of 14 , Oct 1, 2003
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        How abot one-digit-primes? ;-)

        Well there surely are more interesting ones ...

        richyfourtythree


        > 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...
      • chriscard1@netscape.net
        ... Even primes? Chris __________________________________________________________________ McAfee VirusScan Online from the Netscape Network. Comprehensive
        Message 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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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