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Finitude of primes

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  • mad37wriggle
    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.
    Message 1 of 14 , Oct 1, 2003
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      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...


      Richard
    • 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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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