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Re: Finitude of primes

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  • richyfourtythree
    How abot one-digit-primes? ;-) Well there surely are more interesting ones ... richyfourtythree
    Message 1 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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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