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 And cryptographers are fond of them. See RSA encryption. len -----Original Message----- From: Mike Sokolov [mailto:sokolov@ifactory.com] Sent: Friday, July 06, 2012 10:19 AM To: Rushforth, Peter Cc: Dimitre Novatchev; Costello, Roger L.; xml-dev@lists.xml.org Subject: Re: ANN: the first million prime numbers in XML format Oh, Peter. So many things - where to begin? The most basic fact is that every natural number can be written as a product of primes in a unique way. This fact is referred to as the fundamental theorem of arithmetic. The greatest unsolved problem in mathematics, the Riemann hypothesis, can be understood as a statement about the distribution of prime numbers. Why is it the greatest unsolved problem? Because so many other problems are equivalent or related to it in some way, from a great many branches of mathematics. One of my favorite facts about primes is that Zeta(s) = Sum (n=1,inf) n^(-s) is = Prod (p prime) 1/(1- p^(-s)) in other words - an infinite sum over all natural numbers is = to an infinite product over all the primes. But there are so many really simple things that are special about the primes. For example, the Goldbach conjecture: any even number can be written as the sum of two primes. So simple, yet unproven. Another unproven fact: there are an infinite number of prime twins: ie consecutive odd primes. That is mildly surprising since primes become less common (tend to be spaced further apart) as they get bigger. Sorry to dive deeply off topic, there must be better mailing lists for this discussion, but you touched a nerve... -Mike On 07/06/2012 11:03 AM, Rushforth, Peter wrote: > Er, pardon me for asking, but what's so special about prime numbers? > > Thanks, > Peter > ________________________________________ > From: Dimitre Novatchev [dnovatchev@gmail.com] > Sent: July 6, 2012 12:39 AM > To: Costello, Roger L. > Cc: xml-dev@lists.xml.org > Subject: Re: ANN: the first million prime numbers in XML format > > A small correction: > > I was speaking about all the primes less than 50 million, nor about > the first 50 million primes. > > Cheers, > > Dimitre. > > On Thu, Jul 5, 2012 at 4:49 PM, Dimitre Novatchev<dnovatchev@gmail.com> wrote: > >> I have had for years even bigger collections of primes and have used >> them to solve Project Eulet problems entirely with XSLT. >> >> The first 50 million primes occupy 27MB. >> >> The format is more convenient for XSLT: >> >> <xsl:variable name="vcountPrimesLT50M" as="xs:integer" >> select="count($vPrimesLT50M)"/> >> >> <xsl:variable name="vPrimesLT50M" as="xs:integer+" >> select= >> " >> 2,3,5,7,11,13,17,19 >> >> ,23,29,31,37,41,43,47,53 >> >> ,59,61,67,71,73,79,83,89 >> >> ,97,101,103,107,109,113,127,131 >> >> ,137,139,149,151,157,163,167,173 >> >> ,179,181,191,193,197,199,211,223 >> >> . . . . . . >> >> >> If someone is interested, please ping me and I will make these files available. >> >> >> Cheers, >> Dimitre. >> >> On Thu, Jul 5, 2012 at 1:07 PM, Costello, Roger L.<costello@mitre.org> wrote: >> >>> Hi Folks, >>> >>> I often wondered why mathematics books seem so focused on prime numbers. >>> >>> Now I know. >>> >>> Recall what a prime number is: an integer larger than 1 is said to be >>> prime if it cannot be written as a product of two smaller positive integers. >>> >>> Here are some prime numbers: 2, 3, 5, 7, 11, 13. >>> >>> A number that is not prime is said to be composite. Here are some >>> composite numbers: 4, 6, 8, 9, 10, 12. >>> >>> So every positive integer is either a prime or a composite. >>> >>> It can be proven that every composite number can be decomposed into a >>> product of primes. >>> >>> Further, there is only one way to factorize a composite number into >>> primes. This is called the unique factorization theorem. >>> >>> So, the building blocks of every integer beyond 1 are primes. In this >>> sense the primes from mathematics correspond to the atoms from chemistry and >>> deserve the same kind of intense scrutiny. >>> >>> Neat! >>> >>> So I created two XML documents, collectively containing the first million >>> prime numbers. >>> >>> The first XML document contains the first 500,000 primes and the second >>> XML document contains the 500,001 to 1,000,000 prime numbers: >>> >>> http://www.xfront.com/first-500000-primes.xml >>> http://www.xfront.com/second-500000-primes.xml >>> >>> Be patient. They are large files (10 MB and 11 MB, respectively) >>> >>> /Roger >>> >>> _______________________________________________________________________ >>> >>> XML-DEV is a publicly archived, unmoderated list hosted by OASIS >>> to support XML implementation and development. To minimize >>> spam in the archives, you must subscribe before posting. >>> >>> [Un]Subscribe/change address: http://www.oasis-open.org/mlmanage/ >>> Or unsubscribe: xml-dev-unsubscribe@lists.xml.org >>> subscribe: xml-dev-subscribe@lists.xml.org >>> List archive: http://lists.xml.org/archives/xml-dev/ >>> List Guidelines: http://www.oasis-open.org/maillists/guidelines.php >>> >>> >> >> >> -- >> Cheers, >> Dimitre Novatchev >> --------------------------------------- >> Truly great madness cannot be achieved without significant intelligence. >> --------------------------------------- >> To invent, you need a good imagination and a pile of junk >> ------------------------------------- >> Never fight an inanimate object >> ------------------------------------- >> To avoid situations in which you might make mistakes may be the >> biggest mistake of all >> ------------------------------------ >> Quality means doing it right when no one is looking. >> ------------------------------------- >> You've achieved success in your field when you don't know whether what >> you're doing is work or play >> ------------------------------------- >> Facts do not cease to exist because they are ignored. >> ------------------------------------- >> I finally figured out the only reason to be alive is to enjoy it. >> > > > -- > Cheers, > Dimitre Novatchev > --------------------------------------- > Truly great madness cannot be achieved without significant intelligence. > --------------------------------------- > To invent, you need a good imagination and a pile of junk > ------------------------------------- > Never fight an inanimate object > ------------------------------------- > To avoid situations in which you might make mistakes may be the > biggest mistake of all > ------------------------------------ > Quality means doing it right when no one is looking. > ------------------------------------- > You've achieved success in your field when you don't know whether what > you're doing is work or play > ------------------------------------- > Facts do not cease to exist because they are ignored. > ------------------------------------- > I finally figured out the only reason to be alive is to enjoy it. > > _______________________________________________________________________ > > XML-DEV is a publicly archived, unmoderated list hosted by OASIS > to support XML implementation and development. To minimize > spam in the archives, you must subscribe before posting. > > [Un]Subscribe/change address: http://www.oasis-open.org/mlmanage/ > Or unsubscribe: xml-dev-unsubscribe@lists.xml.org > subscribe: xml-dev-subscribe@lists.xml.org > List archive: http://lists.xml.org/archives/xml-dev/ > List Guidelines: http://www.oasis-open.org/maillists/guidelines.php > > > _______________________________________________________________________ > > XML-DEV is a publicly archived, unmoderated list hosted by OASIS > to support XML implementation and development. To minimize > spam in the archives, you must subscribe before posting. > > [Un]Subscribe/change address: http://www.oasis-open.org/mlmanage/ > Or unsubscribe: xml-dev-unsubscribe@lists.xml.org > subscribe: xml-dev-subscribe@lists.xml.org > List archive: http://lists.xml.org/archives/xml-dev/ > List Guidelines: http://www.oasis-open.org/maillists/guidelines.php > > _______________________________________________________________________ XML-DEV is a publicly archived, unmoderated list hosted by OASIS to support XML implementation and development. To minimize spam in the archives, you must subscribe before posting. [Un]Subscribe/change address: http://www.oasis-open.org/mlmanage/ Or unsubscribe: xml-dev-unsubscribe@lists.xml.org subscribe: xml-dev-subscribe@lists.xml.org List archive: http://lists.xml.org/archives/xml-dev/ List Guidelines: http://www.oasis-open.org/maillists/guidelines.php 
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