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I suppose because they're 'hard to guess'. Funny, because I was looking for a way to guess 7 of 7 numbers drawn at random without replacement from 49 :-) Oh well. Peter > -----Original Message----- > From: Len Bullard [mailto:Len.Bullard@s...] > Sent: July 6, 2012 11:30 > To: Mike Sokolov; Rushforth, Peter > Cc: Dimitre Novatchev; Costello, Roger L.; xml-dev@l... > Subject: RE: ANN: the first million prime numbers > in XML format > > And cryptographers are fond of them. See RSA encryption. > > len > > -----Original Message----- > From: Mike Sokolov [mailto:sokolov@i...] > Sent: Friday, July 06, 2012 10:19 AM > To: Rushforth, Peter > Cc: Dimitre Novatchev; Costello, Roger L.; xml-dev@l... > 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@g...] > > Sent: July 6, 2012 12:39 AM > > To: Costello, Roger L. > > Cc: xml-dev@l... > > 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@g...> 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@m...> 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@l... > >>> subscribe: xml-dev-subscribe@l... 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@l... > > subscribe: xml-dev-subscribe@l... 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@l... > > subscribe: xml-dev-subscribe@l... 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@l... > subscribe: xml-dev-subscribe@l... List archive: > http://lists.xml.org/archives/xml-dev/ > List Guidelines: http://www.oasis-open.org/maillists/guidelines.php > >
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