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Polynomial that generates only primes...for the first 51 values

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  • Gary Chaffey
    I have found that 2*x^2-88*x+997 generates primes for x in [0,50].. On the mathworld website I can only find examples which generate upto a maximum of 45
    Message 1 of 6 , Jul 26, 2003
      I have found that 2*x^2-88*x+997 generates primes for
      x in [0,50]..
      On the mathworld website I can only find examples
      which generate upto a maximum of 45 primes.
      Does anyone know of a better second order polynomial
      in one variable???
      Thanks in advance
      Gary

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    • Jens Kruse Andersen
      ... Actually the polynomial generates primes for x in [-6,50]. A simple transformation g(y)=f(y-6) will change this to [0,56]. However the polynomial is
      Message 2 of 6 , Jul 26, 2003
        Gary Chaffey wrote:
        > I have found that 2*x^2-88*x+997 generates primes for
        > x in [0,50]..
        > On the mathworld website I can only find examples
        > which generate upto a maximum of 45 primes.
        > Does anyone know of a better second order polynomial
        > in one variable???

        Actually the polynomial generates primes for x in [-6,50].
        A simple transformation g(y)=f(y-6) will change this to [0,56].
        However the polynomial is symmetric on the range and only generates 29
        distinct primes.
        Euler's x^2+x+41 gives 40 distinct primes for x in [0,39] and 80 symmetric
        primes in [-40,39], which can easily be transformed to [0,79].
        Euler's is the best known as far as I know.

        --
        Jens Kruse Andersen
      • Didier van der Straten
        About Euler s polynomial, you may found an explanation of why it generates this range of prime numbers by looking at my web pages discussing as well the Ulam s
        Message 3 of 6 , Jul 26, 2003
          About Euler's polynomial, you may found an explanation of why it generates
          this range
          of prime numbers by looking at my web pages discussing as well the Ulam's
          spirals phenomenon.

          It is at URL http://www.geocities.com/dhvanderstraten/ulamtxt.html.

          Appreciate any feedback.
          Didier van der Straten

          -----Message d'origine-----
          De : Jens Kruse Andersen [mailto:jens.k.a@...]
          Envoyé : samedi 26 juillet 2003 14:13
          À : primenumbers@yahoogroups.com
          Objet : Re: [PrimeNumbers] Polynomial that generates only primes...for
          the first 51 values


          Gary Chaffey wrote:
          > I have found that 2*x^2-88*x+997 generates primes for
          > x in [0,50]..
          > On the mathworld website I can only find examples
          > which generate upto a maximum of 45 primes.
          > Does anyone know of a better second order polynomial
          > in one variable???

          Actually the polynomial generates primes for x in [-6,50].
          A simple transformation g(y)=f(y-6) will change this to [0,56].
          However the polynomial is symmetric on the range and only generates 29
          distinct primes.
          Euler's x^2+x+41 gives 40 distinct primes for x in [0,39] and 80 symmetric
          primes in [-40,39], which can easily be transformed to [0,79].
          Euler's is the best known as far as I know.

          --
          Jens Kruse Andersen



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        • Dr. Michael Hartley
          Congrats! I noticed your polynomial is also prime for a few negative values of x. By substituting x = t-6, you can get 2*t^2-112*t+1597 which is prime for t in
          Message 4 of 6 , Jul 30, 2003
            Congrats!

            I noticed your polynomial is also prime for a few negative values of x.

            By substituting x = t-6, you can get

            2*t^2-112*t+1597 which is prime for t in [0..56]

            Once again, congrats.. :-)


            -----Original Message-----
            From: Jens Kruse Andersen [mailto:jens.k.a@...]
            Sent: 31 July 2003 02:55
            To: undisclosed-recipients:;
            Subject: Re: [PrimeNumbers] Polynomial that generates only primes...for the first 51 values


            Gary Chaffey wrote:
            > I have found that 2*x^2-88*x+997 generates primes for
            > x in [0,50]



            [Non-text portions of this message have been removed]
          • Jens Kruse Andersen
            ... From: Dr. Michael Hartley To: Jens Kruse Andersen ; Cc:
            Message 5 of 6 , Jul 31, 2003
              Dr. Michael Hartley wrote:

              ----- Original Message -----
              From: "Dr. Michael Hartley" <michael@...>
              To: "Jens Kruse Andersen" <jens.k.a@...>; <undisclosed-recipients:;>
              Cc: <primenumbers@yahoogroups.com>
              Sent: Thursday, July 31, 2003 3:45 AM
              Subject: RE: Re: [PrimeNumbers] Polynomial that generates only primes...for
              the first 51 values


              > Congrats!
              >
              > I noticed your polynomial is also prime for a few negative values of x.
              >
              > By substituting x = t-6, you can get
              >
              > 2*t^2-112*t+1597 which is prime for t in [0..56]
              >
              > Once again, congrats.. :-)
              >
              >
              > -----Original Message-----
              > From: Jens Kruse Andersen [mailto:jens.k.a@...]
              > Sent: 31 July 2003 02:55
              > To: undisclosed-recipients:;
              > Subject: Re: [PrimeNumbers] Polynomial that generates only primes...for the
              first 51 values
              >
              >
              > Gary Chaffey wrote:
              > > I have found that 2*x^2-88*x+997 generates primes for
              > > x in [0,50]
              >

              I have not e-mailed you. Yesterday I also received the mail you quote,
              allegedly from myself!
              Someone on the primenumbers list must have a virus picking addresses from the
              host computer and sending mails in my name. That has happened before for
              others. This stupid virus mailed me with me as sender. The above shows the
              virus gives the sender address jens.k.a@... where my address is
              jens.k.a@...
              The mail I got was 98 kb with an attached file, probably a virus. If anyone
              receives big unexpected mails claiming to come from me then delete them
              without opening them - kind of makes it dangerous to request my tuplet
              finder :-(
              If you have already opened a mail, do a virus scan. The only I have
              sent a true mail with attached files is Paul Jobling. The virus may pick other
              sender addresses so look out.

              --
              Jens Kruse Andersen
            • Mike Oakes
              ... recipients:; ... primes...for ... of x. ... primes...for the ... quote, ... addresses from the ... before for ... shows the ... If anyone ... them ...
              Message 6 of 6 , Aug 1, 2003
                --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
                <jens.k.a@g...> wrote:
                > Dr. Michael Hartley wrote:
                >
                > ----- Original Message -----
                > From: "Dr. Michael Hartley" <michael@k...>
                > To: "Jens Kruse Andersen" <jens.k.a@r...>; <undisclosed-
                recipients:;>
                > Cc: <primenumbers@yahoogroups.com>
                > Sent: Thursday, July 31, 2003 3:45 AM
                > Subject: RE: Re: [PrimeNumbers] Polynomial that generates only
                primes...for
                > the first 51 values
                >
                >
                > > Congrats!
                > >
                > > I noticed your polynomial is also prime for a few negative values
                of x.
                > >
                > > By substituting x = t-6, you can get
                > >
                > > 2*t^2-112*t+1597 which is prime for t in [0..56]
                > >
                > > Once again, congrats.. :-)
                > >
                > >
                > > -----Original Message-----
                > > From: Jens Kruse Andersen [mailto:jens.k.a@r...]
                > > Sent: 31 July 2003 02:55
                > > To: undisclosed-recipients:;
                > > Subject: Re: [PrimeNumbers] Polynomial that generates only
                primes...for the
                > first 51 values
                > >
                > >
                > > Gary Chaffey wrote:
                > > > I have found that 2*x^2-88*x+997 generates primes for
                > > > x in [0,50]
                > >
                >
                > I have not e-mailed you. Yesterday I also received the mail you
                quote,
                > allegedly from myself!
                > Someone on the primenumbers list must have a virus picking
                addresses from the
                > host computer and sending mails in my name. That has happened
                before for
                > others. This stupid virus mailed me with me as sender. The above
                shows the
                > virus gives the sender address jens.k.a@r... where my address is
                > jens.k.a@g...
                > The mail I got was 98 kb with an attached file, probably a virus.
                If anyone
                > receives big unexpected mails claiming to come from me then delete
                them
                > without opening them - kind of makes it dangerous to request my
                tuplet
                > finder :-(
                > If you have already opened a mail, do a virus scan. The only I have
                > sent a true mail with attached files is Paul Jobling. The virus may
                pick other
                > sender addresses so look out.
                >
                > --
                > Jens Kruse Andersen


                Hi
                Today I got the email which follows, which seems to be an
                interception by AOL of a message which was attempting to reach me.
                Maybe its contents are of some use to people who know about viruses
                and suchlike?
                Mike Oakes


                Subj: Returned mail: Service unavailable
                Date: 01/08/03 10:09:09 GMT Daylight Time
                From: MAILER-DAEMON@... (Mail Delivery Subsystem)
                To: jens.k.a@...

                The original message was received at Wed, 30 Jul 2003 14:55:36 -0400
                (EDT)
                from rly-za06.mail.aol.com [172.31.36.108]

                *** ATTENTION ***

                Your e-mail is being returned to you because there was a problem with
                its
                delivery. The address which was undeliverable is listed in the
                section
                labeled: "----- The following addresses had permanent fatal errors ---
                --".

                The reason your mail is being returned to you is listed in the section
                labeled: "----- Transcript of Session Follows -----".

                The line beginning with "<<<" describes the specific reason your e-
                mail could
                not be delivered. The next line contains a second error message
                which is a
                general translation for other e-mail servers.

                Please direct further questions regarding this message to your e-mail
                administrator.

                --AOL Postmaster

                ----- The following addresses had permanent fatal errors -----
                <mikeoakes2@...>

                ----- Transcript of session follows -----
                ... while talking to airmail-02.mail.aol.com.:
                >>> DATA
                <<< 554 TRANSACTION FAILED - Unrepairable Virus Detected. Your mail
                has not been sent.
                554 <mikeoakes2@...>... Service unavailable

                Final-Recipient: RFC822; mikeoakes2@...
                Action: failed
                Status: 5.0.0
                Remote-MTA: DNS; airmail-02.mail.aol.com
                Diagnostic-Code: SMTP; 554 TRANSACTION FAILED - Unrepairable Virus
                Detected. Your mail has not been sent.
                Last-Attempt-Date: Wed, 30 Jul 2003 14:58:52 -0400 (EDT)

                Received: from rly-za06.mx.aol.com (rly-za06.mail.aol.com
                [172.31.36.108]) by str-d02.mail.aol.com (v92.16) with ESMTP id
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                SMTP id h6UIsUX2002553;
                Wed, 30 Jul 2003 20:54:30 +0200
                (envelope-from <jens.k.a@...>)
                Date: Wed, 30 Jul 2003 20:54:30 +0200
                Message-Id: <200307301854.h6UIsUX2002553@...>
                From: "Jens Kruse Andersen" <jens.k.a@...>
                Subject: Re: [PrimeNumbers] Polynomial that generates only
                primes...for the first 51 values
                MIME-Version: 1.0
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                SPVN0HWFLSL28B4"
                To: undisclosed-recipients:;
                X-AOL-IP: 195.238.2.124
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