Prime number/Talk

Links: http://www.utm.edu/research/primes/

The first 750,000 primes: http://www.geocities.com:80/ResearchTriangle/Thinktank/2434/prime/primenumbers.html

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Now here's an interesting question which may even provide a valid use for subpages.

Would adding a list of all the prime numbers known to mankind be counter-productive to the idea of the Wikipedia? It is "a compendium of human knowledge", regardless of how obscure and arcane.

(I suppose one could extend this to listing Pi to a quadrillion digits, to be somewhat hyperbolic.)

Thoughts? --Colin dellow

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I'd say that the encyclopedia should be a compendium of all useful knowledge. Digit number 323454 of Pi and the temperature at noon on May 7, 1976 in Salt Lake City are part of human knowledge, but really, nobody has a use for this information except maybe some highly specialized experts, who know where to look it up.

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I perhaps didn't make my point clear. Wikipedia presents the ability to have "useless" trivia because of the [Wikipedia is not paper]? argument.

Perhaps it will be useful only to a specialised group, but does it hurt to have it? It would increase the amount of information available in the Wikipedia. (I found the comment about temperatures in Salt Lake City at a given year to be somewhat unrelated to this question, BTW.) --Colin dellow

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Actually, I don't think it would be possible to list all the known primes. There are just too darn many of them, and it's too easy to find more. - Hank Ramsey

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Note regarding the proof of the infinitude of primes: we use the fact that every composite number has a prime factor. I think that requires proof in itself.

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Yes, perhaps, if it isn't obvious. It is clear that if a given number has a composite divisor, then the divisors of that divisor are also divisors of the original number (if A=B*C and C=D*E then A=B*D*E). If any of these divisors are composite, we can apply this principle recursively to find more divisors of the original number. We cannot recurse indefinitely because the number cannot have an infinite number of divisors. So eventually we must reach a point where all the new divisors are prime. QED

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sub page or article on infamous research project "A Short List of Even Primes" which is of course, mainly acknowledgements and academic scaffolding, followed by the list, viz. 2

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I wouldn't mind a link to a joke if it's clearly labeled as such. For that matter, I wouldn't mind adding the old "proof" that all primes are odd. -LC

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The article says:

There are infinitely many prime numbers. The oldest known proof for this statement dates back to the Greek mathematician Euclid. It is also one of the oldest known proofs by contradiction.

I thought that Euclid stated the theorem as "Given any prime, there is a larger prime." With the theorem stated like this, the proof isn't a proof by contradiction -- the existence of the larger prime is shown directly. Can someone confirm this, or am I misremembering? --Zundark, 2001 Oct 11

I think you're right; I'll take the contradiction bit out. --AxelBoldt