RE: [xml-dev] ANN: the first million prime numbers in XML format

["Rushforth, Peter" <Peter.Rushforth@NRCan-RNCan.gc.ca>]

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@ses-i.com] 
> Sent: July 6, 2012 11:30
> To: Mike Sokolov; Rushforth, Peter
> Cc: Dimitre Novatchev; Costello, Roger L.; xml-dev@lists.xml.org
> Subject: RE: [xml-dev] 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@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: [xml-dev] 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: [xml-dev] 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
> >>>
> >>>
> ______________________________________________________________
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> >>>        
> >>
> >>
> >> --
> >> 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.
> >
> >
> ______________________________________________________________
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> >    
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