December 2003 - cypherpunks-legacy

Re: Goldbach's Conjecture - a question about prime sums of odd numbers... (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Subject: Re: Goldbach's Conjecture - a question about prime sums of odd numbers... > Date: Thu, 19 Nov 1998 09:26:56 -0600 (CST) > From: ichudov(a)Algebra.Com (Igor Chudov @ home) > > All even numbers greater than two can be represented as the sum of primes. > > Do you mean a sum of DIFFERENT primes? None of the references that I've looked at state it clearly but I assume that it must be or else we could just use 1 for everything. > > Is there any work on whether odd numbers can always be represented as the > > sum of primes? > > Well, take 11, for example, it cannot be repsesented as a sum of different > primes. It cannot, pure and simple. Sure it can, 1 + 3 + 7. It can't be the PRODUCT of two lower primes since it wouldn't be prime then. This sum by the way CAN'T be reduced to two primes so Fermat's Conjecture applied to odds is clearly false. The only proviso is the number we want to sum TO must be greater than 2. ALL numbers can be represented as sums of primes, the question is whether you allow repeats or not. > > This of course implies that the number of prime members > > must be odd and must exclude 1 (unless you can have more than a single > > instance of a given prime). Has this been examined? > > Why, let's say 5 = 3+2, it is a sum of an even number of primes. In the number theory realm, I agree. In the geometric real (in particular using equilateral triangles) those constraints hold. Note that the smallest number of sums for your example above is odd. The reason that you must exclude the problem becomes trivial if you aren't required to sum the 1's. > I suggest that first "examination" should always include playing > with trivial examples. No kidding? > If multiple instances are allowed, it is an enormously boring conjecture > for 5 grade school students. > > any number above 1 may be represented as a sum of some 3s and some > 2s. Big deal. Actualy they are simply sums of 1's, its actualy first grade math. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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Re: Goldbach's Conjecture - a question about prime sums of odd numbers
by Jim Gillogly 17 Dec '03

17 Dec '03

Ray Arachelian wrote: > "Igor Chudov @ home" wrote: > > Well, take 11, for example, it cannot be repsesented as a sum of different > > primes. It cannot, pure and simple. > Bullshit: 7+5+(-1)=11. Last I heard, negative numbers weren't excluded from > being primes. 7 is different from 5, -1 is different from 7 and from 5. If this is boiling down to a definition of primes, I'll haul out my Hardy & Wright, page 2: A number p is said to be prime if (i) p > 1, (ii) p has no positive divisors except 1 and p. ... It is important to observe that 1 is not reckoned as a prime. My number theory class at college (admittedly that was three decades ago) also started the prime series at 2 and went up from there. The term "odd primes" always meant 3 and above, not 1 and above. YMMV. -- Jim Gillogly 29 Blotmath S.R. 1998, 16:29 12.19.5.12.12, 4 Eb 5 Ceh, Ninth Lord of Night

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Re: Goldbach's Conjecture - a question about prime sums of odd numbers (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Date: Thu, 19 Nov 1998 12:18:26 -0500 > From: Ray Arachelian <sunder(a)brainlink.com> > Subject: Re: Goldbach's Conjecture - a question about prime sums of odd numbers > So I guess I have to take back 7+5+(-1) and go with Jim's 1+3+7, but fuck, > that won't work either since 1 isn't a prime... So I guess Igor is right on > this one. Sorry Jim... A prime is defined as *ANY* number (note the definition doesn't mention sign or magnitude nor does it exclude any numbers a priori) that has no multiplicative factors other than itself and 1. 1 * 1 = 1 so it is clearly prime. Now, if a particular branch of number theory wants to extend it and make it only numbers >=2 that is fine, I'm not working in that branch anyway. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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Re: Goldbach's Conjecture - a question about prime sums of odd (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Subject: Re: Goldbach's Conjecture - a question about prime sums of odd > Date: Thu, 19 Nov 1998 10:53:50 -0600 (CST) > From: ichudov(a)Algebra.Com (Igor Chudov @ home) > I have no idea where you heard it, but primes are numbers greater than 1, > by definition. Actualy a prime is any number which has no multiplicitave factors other than itself and 1. Does that mean negatives can't be prime numbers? So, -3 breaks down to: -3 * 1 = -3; 3 * -1 would be another set of factors so negatives can't be primes in the strictest sense. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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Re: Goldbach's Conjecture (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Date: Fri, 20 Nov 1998 18:27:39 +0100 > From: Mok-Kong Shen <mok-kong.shen(a)stud.uni-muenchen.de> > Subject: Re: Goldbach's Conjecture (fwd) > Jim Choate wrote: > > > What started this whole enquiry for me was the realization that the > > multiplication identity axiom is related to the definition of a prime. Then > > add on top of that the reason we exclude 1 is so we don't have to write > > '...except for the prime 1' on the end of lots of number theory (re Richard > > Feynman's comment during the Challenger Investigation). It was the > > realization that if we go ahead and include 1 so the axioms are in line with > > each other (and use our cut&paste feature for the '...1...') then perhaps it > > would provide a more consistent base and just maybe some of the extant > > problems in number theory might become solvable in other ways. My original > If you 'define' 1 to be 'prime', you are 'defining' Goldbach's > conjecture 'away'! Duh. I'll give you a hint, more than that single problem goes away. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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Goldbach Conjecture
by Phillips, Sidney R 17 Dec '03

17 Dec '03

For a reference on the Goldbach Conjecture see: http://www.astro.virginia.edu/~eww6n/math/GoldbachConjecture.html

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[XCERT-ANNOUNCE] Network Associates Relationship (fwd)
by Jim Burnes 17 Dec '03

17 Dec '03

Thought this might be of some interest considering the current NAI thread. jim ---------- Forwarded message ---------- Date: Wed, 18 Nov 1998 13:13:27 -0800 From: Tim Gage <timg(a)xcert.com> To: xcert-announce(a)xcert.com Subject: [XCERT-ANNOUNCE] Network Associates Relationship TO: Xcert Friends and Partners FROM: Thomas Nolan, president and CEO DATE: November 18, 1998 RE: Network Associates Relationship _______________________________________ I'm pleased to report that Xcert International and Network Associates Inc. (NAI) recently announced a technology licensing agreement where NAI will integrate Xcert's software as the default PKI in their Net Tools Secure product suite. This relationship will PKI enable NAI's security offerings-including a suite of best-in-class security applications that encompasses firewall, intrusion protection, vulnerability scanning, encryption, authentication, anti-virus and security management. NAI is a company with approximately $1 Billion in revenue, 5,000 enterprise customers, presence on 60 million desktops and 80% plus penetration into the Global 2000. This is a significant win for Xcert and provides for joint marketing and sales activities, including licensing of certain NAI applications to Xcert, pre-notification of NAI product and technology direction and, most important, the ability for Xcert to work with NAI to sell general purpose PKI into their installed customer base.. Xcert was selected over its competitors because of its superior technology, principally the ability to interoperate with other vendors. NAI's market-leading Total Network Security solution will seed Xcert's technology into the market and will also provide NAI's customers with "hooks" to seamlessly build Xcert's general purpose PKI infrastructure and products into their networks. This is a significant win for Xcert. The NAI adoption of Xcert as their preferred PKI provider adds value to Xcert's brand recognition. This news is yet another compelling endorsement of Xcert's products. In addition, the ability to work with NAI's customer base provides substantial opportunity to Xcert. I am sure you will share my enthusiasm for this momentous milestone on Xcert's road to major market share. ------------------------------------------------------------- For Immediate Release: NETWORK ASSOCIATES TO SHIP COMPREHENSIVE PKI FROM XCERT INTERNATIONAL WITH ALL SECURITY PRODUCT SUITES Network Associates Customers to Receive Scalable Open-Standards Certificate Management Integrated Into Net Tools Secure Product Line SANTA CLARA, Calif., November 17 - Network Associates, Inc. (Nasdaq: NETA) unveiled the next step in its integrated security strategy today by announcing a technology partnership with Xcert International that will bring full open-standards PKI (public key infrastructure) functionality to all Network Associates customers as a standard feature of its integrated security product suites. Beginning in the first quarter of 1999, all integrated security suites from Network Associates will include the new Net Tools PKI server, an enterprise-scaleable PKI server based on Xcert's award-winning digital certificate management technology. "Network Associates has been very aggressive in driving much needed open standards and interoperability in the security space," said Sanjay Kalra, president of Icons, Inc., a leading nationwide PKI consulting firm. "By working with Xcert to include a complete standards-based PKI in all of their security application suites at no extra charge, Network Associates is making things like universal client VPNs and active response firewalls a reality for customers of all sizes. This announcement is the perfect follow-up to their previous PKI partnerships with VeriSign and Entrust." As a result of this partnership, Network Associates customers will be able to broadly deploy integrated security solutions that interoperate through secure and authenticated channels. With this announcement, Network Associates becomes the first vendor to enable secure, scaleable integration between individual security applications by providing flexible PKI functionality out of the box and universally supporting existing PKI solutions like those from partners like VeriSign (Nasdaq: VRSN), Entrust Technologies (Nasdaq: ENTU) and Xcert. Network Associates customers will be licensed to use the new Net Tools PKI with any Network Associates application. Under the terms of the agreement, Network Associates will integrate Xcert's award-winning PKI technology into its Net Tools Secure product line, a suite of best-in-class security applications spanning firewall, intrusion protection, vulnerability scanning, encryption, authentication, anti-virus, and security management. Xcert's flexible open architecture has received multiple industry accolades this year, including a recent Editor's Choice selection from Network Computing that praised Xcert's technology as the "best strategic choice for PKI in the enterprise." Xcert's technology was selected by Network Associates because of its broad support of all industry PKI standards, including x.509, PGP, LDAP, and PKCS #7, 10, and 11. "Network Associates is committed to promoting broad interoperability and open standards in the security industry," said Peter Watkins, general manager of the Net Tools Secure division at Network Associates. "This agreement makes it even easier for our customers to deploy scaleable, standards-based, security applications that work together in concert to actively respond to changing security threats." "This technology license agreement expands Network Associates' best-of-breed security offerings to include the industrial-strength PKI necessary for conducting business-to-business electronic commerce and communications," said Thomas Nolan, President and CEO of Xcert International. "Network Associates customers will be able to broadly deploy distributed security applications, regardless of whether or not they have a general PKI solution. Because Xcert's technology supports all certificate standards, Network Associates customers will also be able to interact seamlessly with business partners who have disparate PKI solutions in use." While other security application vendors have recently discussed plans to integrate their products, none have addressed universal PKI support, an essential element to making integrated security a secure and scaleable reality for enterprise customers. As a result of this agreement, Network Associates customers will be able to broadly deploy distributed security applications such as remote VPN and client-side encryption across large user populations. The new Net Tools PKI will also support more robust certificate management for authenticated communications between integrated Network Associates security applications. Through a concept known as "Active Security", Network Associates is enabling its security products to operate in concert, actively communicating events between applications and adapting security policies of these applications for real-time active response when critical security threats are detected. With headquarters in Santa Clara, California, Network Associates, Inc. is a leading supplier of enterprise network security and management software. Network Associates' Net Tools Secure and Net Tools Manager offer best-of-breed, suite-based network security and management solutions. Net Tools Secure and Net Tools Manager suites combine to create Net Tools, which centralizes these point solutions within an easy-to-use integrated systems management environment. For more information, Network Associates can be reached at (408) 988-3832 or on the Internet at http://www.nai.com. Based in Walnut Creek, California, Xcert International Inc. is the premier developer of Public Key Infrastructure technology. Xcert's products provide privacy and authenticity for conducting secure Internet business transactions. Xcert develops, manufactures and distributes Certificate Authority and public key infrastructure solutions that use secure directory services to provide organizations and individuals with a ubiquitous and secure method of communicating with each other over the Internet. Xcert also licenses its underlying PKI technology to selected service providers and third party developers worldwide. Xcert can be reached on the World Wide Web at http://www.xcert.com. FOR MORE INFORMATION: Ruby Qurashi, Tim Gage Xcert International Inc. 925-274-9300 Ext .108 rubyq(a)xcert.com / timg(a)xcert.com ---------------------------------------------------------------------- XCERT-ANNOUNCE: Xcert Software Announcements Mailing List to remove yourself from this mailing list, please send mail containing "unsubscribe xcert-announce" in the body to majordomo(a)xcert.com

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learn computer forensics with the boys from the US Treasury
by Anonymous 17 Dec '03

17 Dec '03

COURSE TITLE: Computer Encryption/Decryption LENGTH OF PRESENTATION: Lecture Laboratory Practical Exercise Total 2:00 2:00 2:00 6:00 DESCRIPTION: Advancing computer technology, coupled with a growing user awareness of privacy and security issues, has resulted in the widespread use of program, electronic mail, and data file encryption techniques. Today seemingly all sophisticated applications have their own optional encryption schemes including WordPerfect, Word, Lotus, Excel, and a host of others. The computer investigator can expect to encounter encrypted (unreadable) files when examining seized computer evidence. This course demonstrates software tools which will enable the student to decreypt many different files, and examines features of the most commonly used encryption/decryption tool used today: PGP. http://www.ustreas.gov/fletc/ffi/scers.htm

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Math Forum - Ask Dr. Math
by Jim Choate 17 Dec '03

17 Dec '03

http://forum.swarthmore.edu/dr.math/problems/1isprime.html -- -------------------------------------------------------------------- The end of our exploring will be to arrive at where we started, and to know the place for the first time. T.S. Eliot Tivoli Systems James F. Choate 9442 Capital of Texas Hwy. N. 512-436-1062 Austin, Tx. 78759 jchoate(a)tivoli.com -------------------------------------------------------------------- Title: Math Forum - Ask Dr. Math <IMG SRC="http://forum.swarthmore.edu/dr.math/dr.mathQA.gif" ALT="Ask Dr. Math - Questions and Answers from our Archives"> Back to About Numbers || All Levels || Search Dr. Math Why is 1 Not Considered Prime? Date: 20 Mar 1995 12:22:37 -0500 From: ioostind(a)cln.etc.bc.ca (Ian Oostindie) Subject: Why 1 is prime My friend, Roger Gillies told me he received some useful math information from you and gave me your e-mail address. I thought of you when a grade six student stumped me with a classic. Well, at least a classic in my mind. Just recently a grade six student asked me "Why is 1 not considered prime?" I tried to answer but as usual could not since I do not understand this either. I thought it may lie in the fact that "we" don't use the true definition or we are interpreting it wrong. A prime is normally described as a number that can be expressed by only one and itself. We exclude all non-natural numbers from the set that we will be working on and then everything is fine except for when we work with 1. 1 = 1 x 1. That is, one equals 1 times itself and there is no other combination. Now to the grade six student in Faro Yukon, I said there may be a small print clause in the contract with the math gods that says you can only write it once since 1 also equals 1x1x1x1x... This would not work for other primes such as two: 2 does not equal 1x2x2x2x... Likewise, 3 does not equal 1x3x3x3x... Patterns are very important to mathematics, I further explained, and this is a pattern I see being broken. I showed this in a slightly different way to the grade sixer but in essence the same. My question to you, Dr. Math, is what is the small print in the contract with the Math gods and how do we explain it to the grade six kids that are supposed to know it? Thank you very much for any consideration you make. Date: 25 Mar 1995 16:21:45 -0500 From: Dr. Ken Subject: Re: Why 1 is prime Hello there! Yes, you're definitely on the right track. In fact, it's precisely because of "patterns that mathematicians don't like to break" that 1 is not defined as a prime. Perhaps you have seen the theorem (even if you haven't, I'm sure you know it intuitively) that any positive integer has a unique factorization into primes. For instance, 4896 = 2^5 * 3^2 * 17, and this is the only possible way to factor 4896. But what if we allow 1 in our list of prime factors? Well, then we'd also get 1 * 2^5 * 3^2 * 17, and 1^75 * 2^5 * 3^2 * 17, and so on. So really, the flavor of the theorem is true only if you don't allow 1 in there. So why didn't we just say something like "a prime factorization is a factorization in which there are no factors of 1" or something? Well, it turns out that if you look at some more number theory and you accept 1 as a prime number, you'd have all kinds of theorems that say things like "This is true for all prime numbers except 1" and stuff like that. So rather than always having to exclude 1 every time we use prime numbers, we just say that 1 isn't prime, end of story. Incidentally, if you want to call 1 something, here's what it is: it's called a "unit" in the integers (as is -1). What that means is that if we completely restrict ourselves to the integers, we use the word "unit" for the numbers that have reciprocals (numbers that you can multiply by to get 1). For instance, 2 isn't a unit, because you can't multiply it by anything else (remember, 1/2 isn't in our universe right now) and get 1. This is how we think about things in Abstract Algebra, something sixth graders won't need to worry about for a long time, but I thought I'd mention it. -Ken "Dr." Math Submit your own question to Dr. Math <IMG SRC="http://forum.swarthmore.edu/forum.blueline.gif" ALT="_____________________________________"> Math Forum Home || The Collection || Quick Reference || Math Forum Search <IMG SRC="http://forum.swarthmore.edu/forum.blueline.gif" ALT="_____________________________________"> Ask Dr. Math © 1994-1998 The Math Forum This page was created by the Forum SmartPage suite of web tools. Sun Nov 15 23:38:44 1998

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Math Forum - Ask Dr. Math (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

Forwarded message: > Date: Thu, 19 Nov 1998 11:50:34 -0600 > Subject: Math Forum - Ask Dr. Math > http://forum.swarthmore.edu/dr.math/problems/1isprime.html > <META NAME="title" CONTENT="Why is 1 Not Considered Prime?"> > math gods that says you can only write it once since 1 also > equals 1x1x1x1x... This would not work for other primes > such as two: 2 does not equal 1x2x2x2x... Likewise, 3 does > not equal 1x3x3x3x... Whether the 1 is there or not is irrelevant, 3x3x3x3... is not 3 in the first place. 3x1x1x1x1.... IS 3. > Patterns are very important to mathematics, I further > explained, and this is a pattern I see being broken. > Date: 25 Mar 1995 16:21:45 -0500 > From: Dr. Ken > Subject: Re: Why 1 is prime > Yes, you're definitely on the right track. In fact, it's precisely > because of "patterns that mathematicians don't like to break" > that 1 is not defined as a prime. Perhaps you have seen the > theorem (even if you haven't, I'm sure you know it intuitively) > that any positive integer has a unique factorization into primes. > For instance, 4896 = 2^5 * 3^2 * 17, and this is the only possible > way to factor 4896. But what if we allow 1 in our list of prime > factors? Well, then we'd also get 1 * 2^5 * 3^2 * 17, and > 1^75 * 2^5 * 3^2 * 17, and so on. So really, the flavor of the > theorem is true only if you don't allow 1 in there. This definition of a prime has one serious drawback. It ignores the fundamental identity theorem of arithmatic: 1 * n = n So, as a result we're in the interesting and potentialy untenable situation of defining a identity theorem, base our math on it, and then come along one day and say it doesn't apply anymore WITHOUT making any other changes to the structure of the theories.... This is VERY BAD science/math. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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