Mersenne Digest Monday, May 1 2000 Volume 01 : Number 726
----------------------------------------------------------------------
Date: Sat, 29 Apr 2000 00:03:39 EDT
From: "Nathan Russell" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Priority double-checking
Hi,
At Wed, 26 Apr 2000 22:11:58 -0400
George Woltman explained:
>What I do is just re-issue them as first time tests. The last time I did
>this was
>roughly six months ago. I don't feel very guilty about this as there is
>about
>a 50% chance the first test was no good and these exponents probably take
>about half as much time as the big exponents now issued for first time
>testing.
I was merely curious about the status of some of the exponents that I was
seeing. I would certainly agree that re-issuing these as first-time tests
is the best idea. Those who are doing double-checking are presumably doing
so because they feel that the shorter completion times are a fair swap-off
for the decreased chance of finding a prime. They might, as I previously
stated, have some difficulty with completing first-time tests in a timely
manner.
Those doing first-time tests, OTOH, are willing to complete longer runs for
the increased chance of finding a prime. In addition to the factors that
you mentioned, smaller exponents are marginally more likely to be prime. If
anything, when you re-issue the exponents that experienced hardware errors,
you are doing a favor to those who recieve them.
Nathan
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Date: Sat, 29 Apr 2000 02:41:06 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: A conjecture on Perfect numbers
You may have heard this one before, so if you have respond A.S.A.P., OK? All
right. I have conjectured the following statement:
The sum of the following series, ((N)!) / ((k!)((N-k)!)) starting at k=1 to
k=(N), is equal to (2^N). If an odd counterexample is found, then an odd
perfect number exists and has factors that are all distinct, and the number
of factors is N. The only thing I found is N = 0 (0! is 1 here), which is 1,
so the number should be prime. So, the only odd, perfect number is 1, since
the only factors of a prime are itself and one. 2(1) = 1 + 1, so 1 is a
perfect number, if you take this minor exception into consideration.
If anyone has proof of this conjecture, please let me know.
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Date: Sat, 29 Apr 2000 08:58:13 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: A conjecture on Perfect numbers
On 29 Apr 00, at 2:41, [EMAIL PROTECTED] wrote:
> The sum of the following series, ((N)!) / ((k!)((N-k)!)) starting at k=1
> to k=(N), is equal to (2^N). If an odd counterexample is found,
Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
etc etc
where each element (except the 1 at the top) is the sum of the
numbers diagonally above it (blanks count as zero).
In this triangle, the kth element in row n is n! / (k! * (n-k)!).
Why? Because the number of ways of choosing k objects from n is
the same as the number of ways of choosing k objects from (n-1)
_plus_ the number of ways of choosing (k-1) objects from (n-1) -
which gives us the same construction rule as Pascal's Triangle.
It's obvious that the sum of the elements in each row is twice the
sum of the elements in the row above (from the construction
algorithm). Since the sum of the elements in the very first row = 1 =
2^0, it follows that the sum of the elements in _every_ row is a
power of 2 - specifically 2^(n-1), where n is the row number,
counting the very first row as row 1.
There are no counterexamples.
Unfortunately this does not constitute a proof of the non-existence
of odd perfect numbers!
Regards
Brian Beesley
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Date: Sat, 29 Apr 2000 06:32:05 -0700
From: "Simon J Rubinstein-Salzedo" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: A conjecture on Perfect numbers
Good. Now that we are on the topic of perfect numbers, I have proven that
any odd perfect number must have at least 9 factors. Another boy at my
school is trying to tell me that all perfect numbers are in the from
(a^(p-1))(a^p-1), thus showing that there are no odd perfect numbers. Can
someone please explain this to me? I am quite sure that he is wrong.
2^6972593 - 1 is prime.
e^(i*pi) + 1 = 0.
This is the e-mail address of Simon Rubinstein-Salzedo.
When you read this e-mail, Simon will probably be at a math contest.
Don't forget to check Simon's website at http://www.albanyconsort.com/simon
Thanks
SJRS
- ----- Original Message -----
From: <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Friday, April 28, 2000 11:41 PM
Subject: Mersenne: A conjecture on Perfect numbers
> You may have heard this one before, so if you have respond A.S.A.P., OK?
All
> right. I have conjectured the following statement:
>
> The sum of the following series, ((N)!) / ((k!)((N-k)!)) starting at k=1
to
> k=(N), is equal to (2^N). If an odd counterexample is found, then an odd
> perfect number exists and has factors that are all distinct, and the
number
> of factors is N. The only thing I found is N = 0 (0! is 1 here), which is
1,
> so the number should be prime. So, the only odd, perfect number is 1,
since
> the only factors of a prime are itself and one. 2(1) = 1 + 1, so 1 is a
> perfect number, if you take this minor exception into consideration.
>
> If anyone has proof of this conjecture, please let me know.
> _________________________________________________________________
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>
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------------------------------
Date: Sat, 29 Apr 2000 09:18:32 -0500
From: "Richard B. Woods" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Java/javascript anyone?
Eric Hahn wrote:
> I'm converting the numerous 'if' statements into an array lookup,
> and making it calculate out more than just days...
In case you're referring to incorporating calendar knowledge so that you
can deliver year-month-day completion predictions, don't forget that the
Gregorian calendar doesn't have leap years when the year number is
divisible by 100 but not 400. So 2100, 2200, and 2300 (for those 286s
working on the EFF $150,000 prize for a prime >10^8) will not be leap
years, but 2400 will be.
Let's nip Y2.1K errors in the bud. :-)
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Date: Sat, 29 Apr 2000 09:23:17 -0500
From: "Richard B. Woods" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Java/javascript anyone?
In my preceding message, change:
the EFF $150,000 prize for a prime >10^8)
to:
the EFF $150,000 prize for a prime with >=10^8 decimal digits)
:-}
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Date: Sat, 29 Apr 2000 23:36:39 +0800
From: "Dave Mullen" <[EMAIL PROTECTED]>
Subject: Mersenne: Richard's Y2.1K error !!
This is a multi-part message in MIME format.
- ------=_NextPart_000_0020_01BFB233.C401ED00
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Ironic you should mention this, and then make the most common omission.
>From the top, the rules are ...
If year / 100 then leap year
If year / 400 then not leap year
If year / 1000 then leap year
2000 was a Leap Year, as will be 3000 and 4000. Although, as the world's =
spinning is slowing down, maybe we'll need a fourth condition at some =
point in the future ?
Dave
- ------=_NextPart_000_0020_01BFB233.C401ED00
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content=3D"text/html; charset=3Diso-8859-1" =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2614.3500" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Ironic you should mention this, and =
then=20
make the most common omission.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>From the top, the rules are =
...</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>If year / 100 then leap =
year</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>If year / 400 then not leap =
year</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>If year / 1000 then leap =
year</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>2000 was a Leap Year, as will be =
3000 and=20
4000. Although, as the world's spinning is slowing down, maybe we'll =
need a=20
fourth condition at some point in the future ?</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Dave</FONT></DIV></BODY></HTML>
- ------=_NextPart_000_0020_01BFB233.C401ED00--
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------------------------------
Date: Sat, 29 Apr 2000 23:40:09 +0800
From: "Dave Mullen" <[EMAIL PROTECTED]>
Subject: Mersenne: Oops
This is a multi-part message in MIME format.
- ------=_NextPart_000_002D_01BFB234.41B09BC0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
I just shot myself in the foot again. Please ignore the last message. =
This is what happens when I wake up at 3am to read my E-Mail.
Sorry Richard !!
Dave
- ------=_NextPart_000_002D_01BFB234.41B09BC0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content=3D"text/html; charset=3Diso-8859-1" =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2614.3500" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>I just shot myself in the foot again. =
Please ignore=20
the last message. This is what happens when I wake up at 3am to read my=20
E-Mail.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Sorry Richard !!</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Dave</FONT></DIV></BODY></HTML>
- ------=_NextPart_000_002D_01BFB234.41B09BC0--
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------------------------------
Date: Sat, 29 Apr 2000 21:07:39 +0000
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Mersenne: Re: Richard's Y2.1K error !!
On Sat, Apr 29, 2000 at 11:36:39PM +0800, Dave Mullen wrote:
>If year / 100 then leap year
>If year / 400 then not leap year
>If year / 1000 then leap year
OK, to complete the mess (I saw your message saying `ignore this',
but I want to throw in my own errors as well ;-) ):
If year % 4 = 0 then leap year
If year % 100 = 0 then not leap year
If year % 400 = 0 then leap year
If year % 10000 = 0 then not leap year
I don't think there are any more conditions than this, but who knows? :-)
Of course, we're forgetting about the leap SECONDS now...
/* Steinar */
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Date: Sat, 29 Apr 2000 17:29:41 EDT
From: [EMAIL PROTECTED]
Subject: Re: Mersenne: Re: Richard's Y2.1K error !!
In a message dated 4/29/00 2:14:03 PM Pacific Daylight Time,
[EMAIL PROTECTED] writes:
<< I don't think there are any more conditions than this, but who knows? :-)
Of course, we're forgetting about the leap SECONDS now...
>>
Like anyone's going to care about a second or so. Just write it using these
rules. You won't have to worry for another couple of century's. So, If
another rule is found, their is ample time to fix it. So I think it's all
right : - )
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Date: Sat, 29 Apr 2000 17:35:55 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Perfect numbers (Was: A conjecture on Perfect numbers)
Good. Now that we are on the topic of perfect numbers, I have proven that
any odd perfect number must have at least 9 factors. ....
Actually, I had done the same a year ago, showing that an odd perfect number
had to have more than 1, 2, 3, 4, even 5 distinct factors, saying that there
were no exponents, and I got up to the point to the conjecture I showed. It
was with Pascal's triangle, but my proof just said that since you were
dividing 1 into two parts each time, then multiplying by two, then it was
2^n. But that wasn't enough. I'll try and explain my proof in detail in
another e - mail. I'm still working on it.
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Date: Sat, 29 Apr 2000 18:50:07 -0700
From: Stefan Struiker <[EMAIL PROTECTED]>
Subject: Mersenne: Whither PrimeNet Server?
A garland of 404s beyond the / of /ips. Yet results are still received,
and the Entropia Home page displays. Never knew I'd miss the weekend
stats so much.
Sigh,
Stefanovic
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Date: Sun, 30 Apr 2000 08:40:12 +0200
From: Martijn Kruithof <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Whither PrimeNet Server?
Stefan Struiker wrote:
>
> A garland of 404s beyond the / of /ips. Yet results are still received,
> and the Entropia Home page displays. Never knew I'd miss the weekend
> stats so much.
>
> Sigh,
> Stefanovic
prepend www to entropia.com and it works
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Date: Sun, 30 Apr 2000 07:12:42 -0700
From: Russel Brooks <[EMAIL PROTECTED]>
Subject: Mersenne: Top Producers reports?
What's with the Top Producers reports at Entropia.com?
I keep getting 404s for the last couple of days.
Cheers... Russ
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Date: Sun, 30 Apr 2000 16:50:31 +0200
From: Martijn <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Top Producers reports?
Quoting Russel Brooks <[EMAIL PROTECTED]>:
> What's with the Top Producers reports at Entropia.com?
> I keep getting 404s for the last couple of days.
>
> Cheers... Russ
>
replace http://entropia.com with
https://www.entropia.com or http://www.entropia.com
(Some documents need the s, some not)
Kind Regards, Martijn
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Date: Sun, 30 Apr 2000 10:02:37 -0500
From: kilfoyle <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Top Producers reports?
I think the problem is deeper..
Error processing SSI file '/ips/tops.shtml'
and 404's
I bet they will fix it on Monday..
Michael..
Martijn wrote:
> Quoting Russel Brooks <[EMAIL PROTECTED]>:
>
> > What's with the Top Producers reports at Entropia.com?
> > I keep getting 404s for the last couple of days.
> >
> > Cheers... Russ
> >
>
> replace http://entropia.com with
> https://www.entropia.com or http://www.entropia.com
>
> (Some documents need the s, some not)
>
> Kind Regards, Martijn
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Date: Sun, 30 Apr 2000 17:13:09 +0200
From: Martijn <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Top Producers reports?
Quoting kilfoyle <[EMAIL PROTECTED]>:
> I think the problem is deeper..
>
> Error processing SSI file '/ips/tops.shtml'
>
> and 404's
>
> I bet they will fix it on Monday..
>
> Michael..
>
https://www.entropia.com/ips/tops.shtml
works for me, (ignoring some certificate warnings)
yes I also think the problem is deeper, and yes I also
hope this will be fixed on monday. It is merely a
workaround.
> Martijn wrote:
>
> > Quoting Russel Brooks <[EMAIL PROTECTED]>:
> >
> > > What's with the Top Producers reports at
Entropia.com?
> > > I keep getting 404s for the last couple of days.
> > >
> > > Cheers... Russ
> > >
> >
> > replace http://entropia.com with
> > https://www.entropia.com or http://www.entropia.com
> >
> > (Some documents need the s, some not)
> >
> > Kind Regards, Martijn
> >
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Date: Sun, 30 Apr 2000 09:44:42 -0700
From: "Terry S. Arnold" <[EMAIL PROTECTED]>
Subject: Mersenne: Server Problems
I saw a post earlier that claimed that some of the URLs for Primenet needed
a www. in front of entropia.com and others need https instead of http. I
have tried this and am getting either SSI errors of connections refused.
Does anyone know the magic incantations?
Terry
Terry S. Arnold 2975 B Street San Diego, CA 92102 USA
[EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax)
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Date: Sun, 30 Apr 2000 10:38:23 -0700
From: "Terry S. Arnold" <[EMAIL PROTECTED]>
Subject: Mersenne: "Solution" to Server Problem
I believe that I have found the solution to the server problem. When I
substitute 216.120.55.140 in place of www.entropia.com or entropia.com
things work just fine. It appears that there may be either a DNS problem or
a problem with the server itself and I found a back up server. The usual
IP address for both www.entropia.com and entropia.com is 207.104.25.155.
Neither of these responds to a ping. I found this magic IP address when I
noticed that entropia.com web did a refer to 216.120.55.140.
This solved my problem for the time being. I hope they get this fixed tomorrow.
Regards
Terry
Terry S. Arnold 2975 B Street San Diego, CA 92102 USA
[EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax)
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Date: Mon, 01 May 2000 10:27:34 -0700
From: Stefan Struiker <[EMAIL PROTECTED]>
Subject: Mersenne: Iteration 'Count' In Factoring Assignments
TeamG:
I notice a small but increasing number in the iteration count column
of my current factoring assignment. The exponent is 12,xxx,yyy,zzz
and I am using beta 20.4.1 What does this value signify?
Thanks!
Best Regards,
Stefanovic
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End of Mersenne Digest V1 #726
******************************
