Re: Mersenne: Spam (detailed, long, and probably off topic)
Checking my sendmail logs I can confirm the spam orginally came from
192.90.127.17. www.bull.net. Since Bull is a respected company, either
someone broke into their system, or bull doesn't have mail relaying
disabled, and someone is simply relaying via there.
No, not quite.
Time for Spam Fighter 201...
here are the FULL headers...
Received: from acid.base.com (adsl-209-233-24-120.dsl.pacbell.net
[209.233.24.120])
by scruz.net (8.8.5/1.34) with ESMTP id AAA15619
for [EMAIL PROTECTED]; Wed, 17 Mar 1999 00:34:55 -0800 (PST)
(envelope-from [EMAIL PROTECTED])
From: [EMAIL PROTECTED]
Received: (from majordomo@localhost)
by acid.base.com (8.8.5/8.8.5) id VAA12996
for mersenne-outgoing; Tue, 16 Mar 1999 21:52:01 -0800
Received: from www.bull.net (www.bull.net [192.90.127.17])
by acid.base.com (8.8.5/8.8.5) with ESMTP id VAA12992
for [EMAIL PROTECTED]; Tue, 16 Mar 1999 21:52:00 -0800
Received: from pegase.bull.fr (pegase.bull.fr [192.44.49.46]) by www.bull.net
(8.8.2/8.8.2) with ESMTP id GAA70746; Wed, 17 Mar 1999 06:49:48 +0100
Received: from dzbull.frdz.bull.fr (dzbull.frdz.bull.fr [129.184.3.21])
by pegase.bull.fr (8.9.2/8.9.1) with ESMTP id GAA38362;
Wed, 17 Mar 1999 06:35:58 +0100
Date: Wed, 17 Mar 1999 06:35:58 +0100
Message-Id: [EMAIL PROTECTED]
Received: from primus ([208.251.61.175]) by dzbull.frdz.bull.fr
(Post.Office MTA v3.5.2 release 221 ID# 511-52867U100L2S100V35)
with SMTP id fr; Wed, 17 Mar 1999 06:43:28 +0100
To: [EMAIL PROTECTED]
Subject: Mersenne: --= Free Software Club =--
Sender: [EMAIL PROTECTED]
Precedence: bulk
X-UIDL: f6f1c18dd2bd83da11bd17890e05a416
Ok. The first two "Received" headers are merely the list serve rdoing its
thing. The next one is where the list server got the message from
www.bull.net. The next two appear to be internal firewall type relays at
bull.fr The message-id is consistent with this
But, note the LAST Recieved line? "from primus ([208.251.61.175]) by ..." ?
Ok, the 'primus' part is what the spammer's bulk mail program replied with on
the 'HELO' command. But, the part in the [ ]'s was logged by the recieving
server. And guess who 208.251.61.175 is?
$ nslookup -q=PTR 208.251.61.175
... 1Cust175.tnt2.ithaca.ny.da.uu.net
the spammers friend, DA.UU.NET.
The account undoubtably was terminated about 2 hours after the spam was sent,
but since those dialup nodes are used by literally dozens of different ISPs on
a sort of 'lease' basis, and many of these ISP's have free 30 day trial
accounts, the spammer merely needs to sign up again, and pump out as many
relays off of innocent european and asian servers as he can. At least the
dzbull.frdz.bull.fr actually logged the source IP address.
Another relatively new stunt of these spammers Note the advertised
website?
http://3634122867 ?
funny address, eh? Traditional lookup tools tend to choke on those. Well,
convert that decimal integer 3634122867 into hex, and its D89C5073. Now break
that into bytes-er-octets... D8.9C.50.73 Now convert those back to decimal
(ugh, what tangled webs these spammers weave), and its 216.156.80.115. A
$ whois -h whois.arin.net 216.156.80.115
will show its owned by '9netave.com' who is a legitmate ISP and web hosting
company. A bit more poking will discover that this web account has already
been disabled, rendering the spam useless. But, g, the spammers latest
'trick' seems to be to use 1-800 numbers instead of email addresses or
websites, and we have nowhere to complain to ("The Phone Company" ? Hah!)...
Anyways, when I got the spam, I promptly sent my standard complaint form to
... [EMAIL PROTECTED], [EMAIL PROTECTED], and [EMAIL PROTECTED] with a CC: to
[EMAIL PROTECTED] (the Federal Trade Commission claims to use that address to track
unsolicited email activities).
Thanks for your patience. We now return you to your regularly scheduled
programming.
-jrp
Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Spam
On Wed, 17 Mar 1999, Jason Stratos Papadopoulos wrote: As most of you know, Majordomo has always been configured to bounce posts from people who are not subscribed to the list. In the past, this has caught all the spam (and I have saved it all, anybody want copies?) Well, one spam did get through at the dawn of the Age Of Spam. On the heels of this message came another spam. If this pisses you off, you can complain to the postmaster at the ISP responsible. header-reading 101 Look at the full header of the message, all of it. If you don't normally see the full header, use unix mail or configure your reader to show it to you. The first parts is a (possibly large) list of Received: transactions, i.e. Received: from acid.base.com (adsl-209-233-24-120.dsl.pacbell.net [209.233.24.120]) by po2.glue.umd.edu (8.9.3/8.9.0.Beta6) with ESMTP id DAA20440 for [EMAIL PROTECTED]; Wed, 17 Mar 1999 03:35:53 -0500 (EST) From: [EMAIL PROTECTED] Received: (from majordomo@localhost) by acid.base.com (8.8.5/8.8.5) id VAA12996 for mersenne-outgoing; Tue, 16 Mar 1999 21:52:01 -0800 Received: from www.bull.net (www.bull.net [192.90.127.17]) by acid.base.com (8.8.5/8.8.5) with ESMTP id VAA12992 for [EMAIL PROTECTED]; Tue, 16 Mar 1999 21:52:00 -0800 Received: from pegase.bull.fr (pegase.bull.fr [192.44.49.46]) by www.bull.net (8.8.2/8.8.2) with ESMTP id GAA70746; Wed, 17 Mar 1999 06:49:48 +0100 Received: from dzbull.frdz.bull.fr (dzbull.frdz.bull.fr [129.184.3.21]) by pegase.bull.fr (8.9.2/8.9.1) with ESMTP id GAA38362; Wed, 17 Mar 1999 06:35:58 +0100 It's the last Received: line that's of interest, because that's the first server the message was routed through. None of the rest usually matters, since spammers bounce messages all over the place to try and hide their tracks. Likewise, the Reply-To field is always bogus. (Is it becoming clear the sort of people we're dealing with?) Slight correction, it originated with adsl-209-233-24-120.dsl.pacbell.net, a dialup connection, with the rest of the headers faked, so it's actually (in this case) the first of the received lines that are the correct one. Remember that it's only for mailers that follow the rules it's the last Received line that's the originator, spammers don't follow the rules. -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Get the rest there. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: LL testing
[... snip ...] (Interesting, but requires no comment)
M(p) is usually the pth Mersenne number and Mp is 2^p-1 in the
literature. Though occasionally M(p) is used as 2^p-1 on the list. It
could cause confusion only for small p. Is M(3) 2^3-1 or 2^5-1?
Sorry, I'm guilty of this confusion, (though I don't think I'm alone in
this)... Properly, we should be using subscripts (M sub p for 2^p-1)
but this is a text based list.
Also there is a problem in using M(p) for the pth Mersenne prime.
Do we mean the pth numerically or the pth to be discovered?
Several of the known Mersenne primes were discovered out of
numeric sequence. Also, given that double-checking has passed
M(35) but is still quite incomplete in the gap up to 2^2976221-1, I
would consider it makes sense to use provisional names "Spence's
Number" and "Clarkson's Number" for the two known Mersenne
primes bigger than M(35) = 2^1398269-1, until double checking is
complete.
I'm also guilty of confusion between "Mersenne number" meaning a
number of the form 2^p-1 for some prime p and a prime number of
the form 2^p-1. I prefer the former definition, on the basis that (a)
"Mersenne prime" is an obvious replacement for "prime number of
the form 2^p-1", (b) some of the numbers 2^p-1 Mersenne was
interested in (surely "Mersenne numbers" if the term has _any_
meaning) turned out to be composite, despite p being prime.
did Lucas use his test by hand? I know he did it by
hand, at the very least.
I don't know about Lucas. Read some of the articles in Luke's
bibliography, it is a wonderful history. Lehmer and Uhler used desk
calculators. Uhler made many calculations of logarithms and powers,
see for example http://www.scruznet.com/~luke/lit/lit_019.htm
Though poor Uhler had been doing LL-tests in the gap between M127 and
M521.
I deliberately tested 2^31-1 using decimal hand calculation as an
exercise in arithmetic. I can see that using a board with p columns
would be a way of taking advantage of the binary nature of the
problem - in particular, it makes reducing modulo 2^p-1 easy - but
testing 2^127-1 would still take a time on account of the sheer
number of marks to be made (or beans counted, or whatever). If
you have an aptitude for doing arithmetic in octal or hexadecimal,
that would probably be most efficient.
The major problem with hand calculation is that mistakes happen.
(Imagine a computer that makes a random error with a probability
of 1% each time an instruction is executed...) I avoided wasting
time by checking each stage by "casting out nines", this detects
single digit errors, but not neccessarily multiple errors in a
calculation, or transposition errors.
STL137 asks in his post if there is a test similiar to the LL test for
numbers of the form 2^N-k where k=3,5,7, A primality test of the
Lucasian type depends on the factorization of N+1, so I guess not.
However, for some k*2^N-1 there is a primality test that uses the familiar
S{n} = S{n-1}^2-2 differing only in the starting value S{0}. See
Riesel, "Prime Numbers and Computer Methods of Factorization" for example.
In Knuth vol 2 (3rd ed) one of the worked examples refers to this.
(My copy is not to hand at present, so I can't give a detailed
pointer, but it's obvious enough if you follow the references to
"Lucas, Edouard" in the index)
I guess that the problem in practical implementation is that you
don't felicitously get calculation mod k*2^N-1 from the FFT unless k
happens to be 1.
Regards
Brian Beesley
Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: How to factor further?
I got the idea to do some factoring with my now slower-than-average machine (a P133), but I don't want to factor at the current assignments (in the 9M range); instead I would like to fill up the factor limits of small exponents to some common value (56 bits or 58 bits or so). Of course, doing it manually using "Advanced - Factor" is out of question, so I thought to create appropriate entries in worktodo.ini and send the results unsolicited :-) to the PrimeNet server. However, I seem to hit the automatic factor limit value in Prime95, or something else: Error: Work-to-do-file contained bad factoring assignment: 65537,56 Is it possible to do what I am trying? Cornelius Caesar Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: RE: Mersenne Digest V1 #534
Almost no spam gets sent with the tacit approval of the underlying ISP, and most ISPs are anxious to kill spammers. The more people who complain, the better. Apologies if I insulted anyone's intelligence; I'm posting this on the off-chance someone doesn't know it already. jasonp Thanks for the post. This site is the best I have for learning, and I'm not insulted in the least (yet). George Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
RE: Mersenne: How to factor further?
I got the idea to do some factoring with my now slower-than-average machine (a P133), but I don't want to factor at the current assignments (in the 9M range); instead I would like to fill up the factor limits of small exponents to some common value (56 bits or 58 bits or so). If what you want to do is find factors, rather than just planting a marker at a rather arbitrary limit, I'd recommend that you turn to ECM factoring. For example, if you run a couple of thousand curves with a B1 limit of a million, you will very probably find all factors under 100 bits --- vastly in excess of what you will be able to do by trial division. No-one can guarantee that you won't miss one of, say, 70 bits but the odds are very much in your favour. I'll leave it to others to calculate the exact probability. I'm running ECM on a P166 laptop; it found a 102-bit factor of M1201 after a few hundred curves with B1=1 million. Paul Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Re: Mersenne Digest V1 #533
Hi folks There is a technique for assessing the "naturalness" of economic data. This technique, known as Benford's Law, demonstrates that the first digits of naturally occurring phenomena do not occur with equal frequency. In fact, lower digits occur with greater frequency in tabulated natural data than larger digits. Great approach to this from Rodolfo... Benford's Law is visually familiar to those of us old enough to remember such anachronisms as tables of logarithms and slide rules! Statistically, it's because models of natural processes (say, radioactive decay and general "time between" distributions) yield an exponential decaying Poisson distribution. From a computing point of view, it's the same effect as what happens if you generate floating-point numbers of "random" bits, the distribution is skewed (the probability a number is between 1 and 2 is the same as it is between 2 and 4). Pick a (unbounded) random number... how can you do it? You can't make all numbers to infinity equally probable, and any smooth trnasform of the number picked should be "equally random" and have the same distribution. The answer turns out to be logarithmic, hence Benford's Law. (It may be apocryphal, but apparently some 8-bit machine (perhaps Atari?) had a means of generating "random" numbers because some memory location was subject to "noise" - effectively some component acted as a radio antenna. It may even have been by design... but of course results obtained by sampling this location for random bits were awful. Being natural they were not only non-uniform and non-independent but also subject to their surroundings. Can anyone validate this?). Anyway, such logarithmic behavior is certainly visible in the Mersenne data. Heuristically, the probability N=2^n-1 is prime is going to be proportional to 1/log N, ie proportional to 1/n. (we ignore constraints such as n needing to be prime and the factors being of specific form, but this is a good enough start). Hence theoretically we expect the number of Mersenne primes of exponent less than L to be a partial sum of this, proportional to log L. Hence we expect the n'th Mersenne prime to have an exponent increasing exponentially, and, in reverse, the logarithms of the exponents should be statistically regularly spaced. (What follows may be *very* sensitive to a better model of the distribution, but this will do as a first estimate). In an argument similar to Benford's Law, the fractional part of these logarithms should, for a "random" phenomenon, be uniformly distributed on [0,1). If the phenomenon is truly random, then this result should hold no matter what base of logarithm we choose. However, consider plotting the statistical deviation of such observations from randomness for different bases of logarithm. Any marked deviation from statistical "noise" and sampling error is a good indicator of non-random data for which the logarithm base is some sort of controlling parameter. (In effect this is a similar approach as curve fitting our expected distribution model to the observed data). I'd be interested to hear from anyone who constructs such a statistical deviation vs logarithm base plot. We may expect such a statistical approach to suggest a distribution where the overall scaling, and artifacts such as Noll's islands, manifest themselves in the plot as large deviations from randomness and spikes in the plot. This is one for the statisticians, to create a suitable measure of the deviation of these fractional parts from a uniform distribution on [0,1). Perhaps the sample variance will be a good first measure, but with only 37 samples and a high degree of non-independence, beware! Chris Nash Lexington KY UNITED STATES Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: Continuation file format
Would someone please tell me where in the pxxx, qxxx continuation files the iteration count is located? Thank you. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
