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

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• 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???
Gary

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• ... 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
• 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
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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• 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]
• ... 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:;>
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
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

--
Jens Kruse Andersen
• ... 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:;>
> 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
> 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
> 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
--".

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.

--AOL Postmaster

<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)

[172.31.36.108]) by str-d02.mail.aol.com (v92.16) with ESMTP id
RELAYIN2-33f2814a7344; Wed, 30 Jul 2003 14:55:36 -0400
[195.238.2.124]) by rly-za06.mx.aol.com (v95.1) with ESMTP id
MAILRELAYINZA69-6fb3f281481c9; Wed, 30 Jul 2003 14:54:58 -0400
[80.201.36.104])
by gallantin.skynet.be (8.12.9/8.12.9/Skynet-OUT-2.21) with
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
Content-Type: multipart/alternative; boundary="----------
SPVN0HWFLSL28B4"
To: undisclosed-recipients:;
X-AOL-IP: 195.238.2.124
X-AOL-SCOLL-SCORE: 0:XXX:XX
X-AOL-SCOLL-URL_COUNT: 0
Your message has been successfully submitted and would be delivered to recipients shortly.