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Twin Prime Proof Proffered

Posted by samzenpus on from the is-this-going-to-be-on-the-test dept.

HateBreeder writes "Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many Prime Twins, it seems that a hole has recently been found in the proof, however mathematicians remain hopeful that the proof can be corrected."

179 comments

  1. Withdrawn by Agret · · Score: 5, Informative

    The paper has since been withdrawn with the reason "A serious error has been found in the paper, specifically, Lemma 8 is incorrect."

    --
    Have you metaroderated recently?
    1. Re:Withdrawn by millwall · · Score: 0

      So perhaps the Slashdot post should be withdrawn as well since tere is nothing new here. Move along.

    2. Re:Withdrawn by metlin · · Score: 4, Informative


      Yeah, it's likely it'll take a long time to fix it.

      Gerald Tenenbaum (the guy who pointed out the mistake) is quite well known, so if he feels that this affects the paper badly, it's probably quite true - and it maybe a while before people get around coming up with an alternative.

      (I know this because Tenenbaum is known to my advisor, Jean Bellissard.)

    3. Re:Withdrawn by Silverlancer · · Score: 0, Redundant

      This sounds very similar to what happened to the proof of Fermat's Last Theorem--hopefully just like with FLT they'll be able to find a way around the problem.

    4. Re:Withdrawn by kimmerin · · Score: 1, Funny

      And who showed that Lemma 8 of the proof is incorrent? G. Tenenbaum of the Institut Élie Cartan in Nancy, so it's a French Fried Proof.

    5. Re:Withdrawn by gartogg · · Score: 3, Interesting

      I understand that it's flawed, but Is there any place the original (flawed in lemma 8) proof can be viewed?

      (I went to GA Tech for a semester...)

      --
      I'm a concientious .sig objector.
    6. Re:Withdrawn by metlin · · Score: 4, Informative

      Here is the original paper.

      (it might be gone soon, though - it's an arXiv mirror)

      Lemma 8 is on Page 35 -


      Lemma 8 Let r(v) and (v) of class C1(v0,), 0 r(v) v0 = 1/2 N0; and let (v) in C0(v ,) be such that

      *defines an integral limit for K as a function of (T) for certain values of T, and gives the boundary and limit conditions*

      Although this made sense, the proof is kinda over my head, though. :-)

      Btw - which dept were you at GT?

    7. Re:Withdrawn by metlin · · Score: 0

      Bah, Slashdot ate up all the variables and constants that I'd copy/pasted from the PDF - too bad.

      You can get it off the paper, anyway.

    8. Re:Withdrawn by bersl2 · · Score: 1

      Props for Bellissard. I'm going to his Calc. II Honors lecture in 30 minutes. Why he was chosen to teach the clueless freshmen, I don't know. He probably has better things to do than watch us stare blankly back at him.

    9. Re:Withdrawn by metlin · · Score: 2, Informative

      Bellissard seriously rocks.

      He's one of the people responsible for theoretical QC research in GATech -- along with Chapman and a few other folks from GTRI such as John Cortese.

      He's also the former editor of the really respected Theoretical Physics journal, Annales de l'Institut Henri Poincaré.

      Brilliant professor, and a wonderful person.

    10. Re:Withdrawn by TheOtherChimeraTwin · · Score: 2, Funny

      Before they patch the problem, what are the chances that someone will develop an exploit? And will that let them root the system?

    11. Re:Withdrawn by Anonymous Coward · · Score: 0

      Ah, yes. The classic proof by proof by eminent authority. Of course it will take a long time to fix it.

    12. Re:Withdrawn by Silverlancer · · Score: 1

      Mod parent REDUNDANT? This was the first post of its type in the thread, albeit perhaps not the last--how in hell can it be redundant?

    13. Re:Withdrawn by sjwaste · · Score: 1

      Because that's what good professors do. You're more likely to stay in the program if you get some exposure to the top names at the school.

      I believe Richard Feynman was known to teach first years as well, and he's one of the most important names in physics this century. You think those freshman physics majors in his class were more or less likely to drop out of the program after meeting that guy? Man, I wish I had been college-age when he was still alive and teaching!

  2. I like a good alliteration as much as anyone by Anonymous Coward · · Score: 5, Informative

    Probably more than most. Sadly, that's not what proffered means.

    It was proffered a long time ago. The news is that it doesn't work. May I suggest punctured?

    1. Re:I like a good alliteration as much as anyone by Agret · · Score: 2, Informative

      To offer for acceptance; tender. See Synonyms at offer.

      The act of proffering; an offer.

      2. To essay or attempt of one's own accord; to undertake, or propose to undertake

      --
      Have you metaroderated recently?
    2. Re:I like a good alliteration as much as anyone by dnoyeb · · Score: 0, Offtopic

      are you agreeing or disagreeing with the coward? I would have been more clear if you offered some of your own text and not just copied the dictionary entry.

      In any event the coward is correct, proffered is not the proper word to use in this case.

    3. Re:I like a good alliteration as much as anyone by weierstrass · · Score: 1

      pranged?

      --
      my password really is 'stinkypants'
    4. Re:I like a good alliteration as much as anyone by palantir · · Score: 1, Funny

      A Better headline would be:
      Two Prime Proof Poofed

    5. Re:I like a good alliteration as much as anyone by reverseengineer · · Score: 4, Interesting
      It was proffered a long time ago. The news is that it doesn't work. May I suggest punctured?

      A couple years ago, there was a proposed proof to the Poincare conjecture- not the Perelman proof which AFAIK still holds together, but another attempt which was soon found to have an insurmountable problem. When the proof was first announced, the Mathworld news item ran, Poincaré Conjecture Purportedly Proved, and when the hole in the proof (essentially, an unproven step used in the proof) came to light, the headline was Poincaré Conjecture Purported Proof Perforated.

      --
      "FDA staff reviewers expressed concern about the number of patients who were left out of the study because they died."
  3. Get MIT on the line, ASAP! by dabigpaybackski · · Score: 5, Funny
    Who's that weird janitor kid who keeps doing equations on the hallway chalkboards? Maybe he could help out with this.

    --
    "OH SHIT, THERE'S A HORSE IN THE HOSPITAL!"
    1. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 0

      HAHAHA!

      Mods on crack, eh?

      Matt Damon acted in Good Will Hunting - the above poster is just making fun of how Matt Damon was portrayed in Team America.

      Heh, some people can't get the bloody joke.

    2. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 0

      Will Hunting

      quit watching movies and read a godamn book

    3. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 2, Funny

      Yeah, this is actually the one time that Matt Damon is ON TOPIC...

    4. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 5, Funny

      since when has a maths nerd known where there are infinitely many prime twins!

    5. Re:Get MIT on the line, ASAP! by metlin · · Score: 1

      quit watching movies and read a godamn book

      Really?

      As a matter of fact, I do.

    6. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 0

      If I see a +2 or 3 Funny and I agree, I mod insightful or interesting to cancel out the retarded twats who mod anything they don't get as offtopic. I don't see why funny doesn't effect karma anyway, but that's a different issue.

    7. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 0

      or even where just one pair of prime twins are?

    8. Re:Get MIT on the line, ASAP! by metlin · · Score: 1

      It's just a personal list - it's written in Excel and exported as HTML.

      Btw, it works fine on both Firefox and Mozilla 1.7.3 - do a refresh and it renders fine.

    9. Re:Get MIT on the line, ASAP! by julesh · · Score: 1

      since when has a maths nerd known where there are infinitely many prime twins!

      Unfortunately, the proof was only that there _are_ infinitely many of them. Actually finding them is left as an exercise to the reader.

    10. Re:Get MIT on the line, ASAP! by Anonymous Coward · · Score: 0

      So Excel puts out this piece of shit HTML? And people actually shell out money for this crap that Microsoft is incompetent to fix? Thanks for letting me know so I'll stay away from it.

    11. Re:Get MIT on the line, ASAP! by IvoryRing · · Score: 1

      It renders poorly for me on Firefox/0.10.1. How you do or should view the impact of that reflection on you is a matter I leave as an exercise for the student.

    12. Re:Get MIT on the line, ASAP! by metlin · · Score: 1

      Actually, it's not meant to be a public list -- the AC asked me if I read books and I just gave him the list.

      It's just something I use personally to keep track of my books.

      But it's funny that it does not render well in FF 0.10 and it seems fine. Weird.

    13. Re:Get MIT on the line, ASAP! by d34thm0nk3y · · Score: 1

      since when has a maths nerd known where there are infinitely many prime twins!

      Proffered Prime Twins Proof Porn?

    14. Re:Get MIT on the line, ASAP! by metlin · · Score: 1

      Not really, but have heard of it. Will check it out, thanks!

  4. /. version by cheezemonkhai · · Score: 5, Funny

    "Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many First Posts, it seems that a hole has recently been found in the proof, however mathematicians remain hopeful that the proof can be corrected."

  5. old news by Anonymous Coward · · Score: 5, Informative

    The mistake was found back in June

    1. Re:old news by gnalle · · Score: 5, Interesting
      A simple Google search reveals that the story is a dupe. Search the old threads for cool comments to boost your karma :)

      When I get more time I want to make a perl script that wgets slashdot.org once an hour and searches google for dupes. It is probably enough to test if any links from present slashdot stories have appeared on the site before, but perhaps I can find a way to pick out relevant title words. Once my script has found a dupe it should pick a few highrated comments from the old thread and repost them :)

    2. Re:old news by charliesmagic · · Score: 1

      There are infinitely many twin comments?

      --

      Charlie's Magic

    3. Re: old news by Anonymous Coward · · Score: 0
      wow.. I posted a wrong comment, and I got modded up. You corrected me and subsequently you were modded offtopic :) Thank you for the correction btw..

      Grandparent poster (Not wanting to jeopardize my karma)

    4. Re:old news by Anonymous Coward · · Score: 0

      Actually, this isn't a dupe. Or at least, it isn't a dupe of the story you pointed out. That story was about a *different* error found in a *different* proof that was only related to the twin prime conjecture, rather than a proof of the conjecture itself.

      Google seems to have failed you today.

  6. Tenenbaum? by Vo0k · · Score: 2, Funny

    While Arenstorf's approach looks promising, an error in one particular step of the proof (...) has recently been pointed out by (...) Tenenbaum

    Damn him, he claims Linux design is wrong too!

    err, does he?

    --
    Anagram("United States of America") == "Dine out, taste a Mac, fries"
    1. Re:Tenenbaum? by nbert · · Score: 2, Insightful

      G. Tenenbaum != Andrew S. Tanenbaum

      --
      I don't read replies by ACs.
    2. Re:Tenenbaum? by Vo0k · · Score: 1

      50% Funny
      40% Overrated
      10% Informative

      Try getting more negative karma from a single post, trolls!

      --
      Anagram("United States of America") == "Dine out, taste a Mac, fries"
    3. Re:Tenenbaum? by Quixote · · Score: 1

      Not the same guy; this one appears to be royalty.

    4. Re:Tenenbaum? by Anonymous Coward · · Score: 0

      Btw, tanenbaum means christmas tree in german.

    5. Re:Tenenbaum? by Anonymous Coward · · Score: 0
      I'd say that it means fir tree if the context isn't related to christmas.

      Also note that the german word is Tannenbaum (yes, I'm nitpicking)

    6. Re:Tenenbaum? by nbert · · Score: 1
      My reply to your post:

      A user has moderated your comment "Informative" (+1).
      It is currently scored Informative (2)

      A user has moderated your comment "Overrated" (-1).
      It is currently scored Informative (1).

      A user has moderated your comment "Insightful" (+1).
      It is currently scored Insightful (2).

      A user has moderated your comment "Insightful" (+1).
      It is currently scored Insightful (3).

      A user has moderated your comment "Overrated" (-1).
      It is currently scored Insightful (2).


      I never heard anyone shouting this here: burn points, burn!

      Let's call it return of the modwars ;)
      --
      I don't read replies by ACs.
    7. Re:Tenenbaum? by Vo0k · · Score: 1

      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Informative (+1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
      A user had given a moderation of Funny (+1) to your comment, Tenenbaum?,
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Funny (+1).
      Tenenbaum?, posted to Twin Prime Proof Proffered, has been moderated Overrated (-1).

      Informative +1 Karma +1
      Funny +5 Karma +0
      Overrated -4 Karma -4
      Final score Funny +2, Karma -3

      --
      Anagram("United States of America") == "Dine out, taste a Mac, fries"
  7. I love.... by Ingolfke · · Score: 5, Funny

    scientists doing math,
    slashdotters aimless wrath,
    comments from stupid jerks,

    and TWINS!

    1. Re:I love.... by bhima · · Score: 1, Funny
      That is just beautiful! This deserves more than +5 funny as it is the best post I've read on /. in months...

      Oh wait, that sort says something about us doesn't it.

      --
      Nothing in the world is more dangerous than sincere ignorance and conscientious stupidity.
    2. Re:I love.... by gowen · · Score: 1

      Yeah, but its still 7am on the Eastern Seaboard, and no one outside North America has ever seen that Coors advert.

      --
      Athletic Scholarships to universities make as much sense as academic scholarships to sports teams.
    3. Re:I love.... by bhima · · Score: 0, Offtopic

      Hah, I now live in the EU and it's almost 2:00 pm!

      --
      Nothing in the world is more dangerous than sincere ignorance and conscientious stupidity.
    4. Re:I love.... by Xiver · · Score: 0, Offtopic

      I know this will probably get a -1 country music modifier, but...

      Reminds me of an old Tom T. Hall Song...

      I love little baby ducks, old pick-up trucks, slow-moving trains, and rain
      I love little country streams, sleep without dreams, sunday school in may, And hay
      And I love you too

      I love leaves in the wind, pictures of my friends, birds in the world, and squirrels
      I love coffee in a cup, little fuzzy pups, bourbon in a glass, and grass,
      And I love you too

      I love honest open smiles, kisses from a child, tomatoes on the vine, and onions
      I love winners when they cry, losers when they try, music when it's good, and life
      And I love you too

      --
      10: PRINT "Everything old is new again."
      20: GOTO 10
    5. Re:I love.... by MegaFur · · Score: 1

      Ah yes, a take on the Oscar the Grouch song. Good song, it deserves more play.

      --
      Furry cows moo and decompress.
    6. Re:I love.... by BeerCur · · Score: 1

      So now that Twin Prime is Proffered... is it now time put down the chalk and watch some football? I love Football on TV Shots of Gena Lee Playing with my friends And Twins I love Burritos at 4 am Parties that never end Dogs that love cats And Twins And I love you too (Here's to Love Songs!)

      --
      It's not what your Sig can do for you, but what you can do for your for your Sig.
    7. Re:I love.... by PetoskeyGuy · · Score: 1

      but can You Prove It?

    8. Re:I love.... by abb3w · · Score: 1

      So, why didn't you double post this?

      --
      //Information does not want to be free; it wants to breed.
  8. twin primes. by rubberbando · · Score: 4, Interesting

    Before I go into my spiel, I will admit that I am no scientist or mathematician.

    I always have had an obsession with the pattern of prime numbers. Now and then I get motivated and download a current list of those discovered. With that I try to find some magical pattern, in hopes of finding a secret message or formula explaining reality. When that announcement was made in the previous slashdot story, I did find the claim of infinite primes to be troubling. From my own observations, I believe the gaps between primes may fluctuate greatly but the maximum and minimums grow ever higher. To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?

    --
    DEAD DEAD DEAD DELETE ME
    1. Re:twin primes. by Moderatbastard · · Score: 1, Insightful
      maximum and minimums grow ever higher
      It's maxima and minima. And I would have thought that the latter tend to grow ever lower...
      --
      1/3 of jokes get modded OT. If you get the joke, mod 1 in 3 insightful/interesting/underrated to restore karma balance.
    2. Re:twin primes. by fymidos · · Score: 3, Informative

      >claim of infinite primes to be troubling

      it is not a claim, it was proven a long long time ago.
      This proof is about infinite number of "prime twins" , primes that are next to each other (like 11-13)

      --
      Washington bullets will simply be known as the "Bulle
    3. Re:twin primes. by isometrick · · Score: 4, Informative

      I think the average maximum difference between primes may increase as primes grow higher (prime density decreases), but twin primes (primes of form p and p+2) continue to exist so the minimum difference for any range can still be very low. IMHO, numerology should be treated like any other -ology, but I did find one reference to what you are talking about: The Music of the Primes, however the site seems to be gone/down. Good luck with your search!

    4. Re:twin primes. by metlin · · Score: 2, Informative

      IMHO, numerology should be treated like any other -ology,

      Errr, numerology is more of a mystical study, considered to be pseudoscience.

      Perhaps you meant Number Theory?

    5. Re:twin primes. by Anonymous Coward · · Score: 0
      From my own observations, I believe the gaps between primes may fluctuate greatly but the maximum and minimums grow ever higher. To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?

      Are you stoned?

    6. Re:twin primes. by rubberbando · · Score: 1

      it is not a claim, it was proven a long long time ago. This proof is about infinite number of "prime twins" , primes that are next to each other (like 11-13)

      My bad. I meant infinite twin primes, not infinite primes.

      --
      DEAD DEAD DEAD DELETE ME
    7. Re:twin primes. by isometrick · · Score: 1

      I meant numerology. I think that finding music in the primes qualifies as numerology.

    8. Re:twin primes. by Lifewish · · Score: 1, Interesting

      Good summary from a waveform perspective.
      There are definitely an infinitely large number of primes. Proof: assume a finite number of primes p1,p2,...,pn (counting from smallest to largest). Then p1*p2*...*pn + 1 is divisible by none of these (hence is prime) and is larger than pn. This is a contradiction of the original assumption, which must therefore be wrong. Hence there are an infinite number of primes.

      --
      For the love of God, please learn to spell "ridiculous"!!!
    9. Re:twin primes. by Anonymous Coward · · Score: 0

      >> I did find the claim of infinite primes to be troubling.

      There are infinitely many primes - that's a really old, really easy proof that people in discrete math courses everywhere do on homeworks. You can find it in any undergrad into to discrete math text.

      The article is talking about twin primes.

    10. Re:twin primes. by metlin · · Score: 2, Informative

      Ah, my bad. I thought you were talking of Primes in P w.r.t. numerology, and being a physicist completely ignored the rest of the content =)

      Been up all night, need more sleep.

      No. %s/g/sleep/coffee. Better!

    11. Re:twin primes. by Kjella · · Score: 4, Interesting

      First, I assume you mean twin primes. Proving infinite primes is trivial and from ancient Greece. It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps). And that primes get rarer and rarer, in the limit, infinitely rare. Neither of those means that the number of primes is finite.

      Basicly, if you set it up as a probability statement:
      p( prime ) -> 0
      p( prime pair ) -> 0

      The latter will simply go towards 0 a lot faster than the former. All you would need to prove is that there must be one more pair (which is not trivial) and you're done.

      Take the greek proof, where you multiply all known primes and add 1. Imagine if you took say, the 1000 smallest primes. All it proves is that there's a prime q <= p1*p2*....*p999*p1000+1. That product will be much much greater than any one of the primes. All it takes it one in the entire interval, and the total is infinite.

      Kjella

      --
      Live today, because you never know what tomorrow brings
    12. Re:twin primes. by Psionicist · · Score: 1

      To me these gaps look like some sort of waveform. If I had better coding skills in the manipulation of sound, I would write a program to generate a sound wave out of these numbers. Does anyone know if this has been tried and if so, what was discovered?

      "All your base are belong to us" in a slightly annoyed British accent.

    13. Re:twin primes. by locofungus · · Score: 2, Interesting

      It's trivial to prove that there is an arbitrarily long sequence of numbers with no primes in it.

      (n+1)!+2 ... (n+1)!+n+1 is a run of n numbers none of which are prime.

      Of course, this doesn't mean that you have to go all the way to (n+1)! before you can find a run of n numbers without a prime, merely that such a run must exist.

      --
      God said, "div D = rho, div B = 0, curl E = -@B/@t, curl H = J + @D/@t," and there was light.
    14. Re:twin primes. by maxwell+demon · · Score: 1

      Since the gap between two primes cannot get smaller than the gap between 2 and 3 (i.e. no number in between at all), the minimum gap is actually a constant function as soon as you passed 3 (and undefined before, of course).

      Now, giben that primes with only one number in between are called twin primes, what about 2 and 3, which are even closer, with nothing in between? Maybe siamese twin primes?

      --
      The Tao of math: The numbers you can count are not the real numbers.
    15. Re:twin primes. by TuringTest · · Score: 1

      The site seems to still be available at the Web Archive:

      --
      Singularity: a belief in the "God" idea with the "demiurge" relation inverted.
    16. Re:twin primes. by miskatonic+alumnus · · Score: 2, Informative

      You cannot conclude that p1*...pn+1 is prime. For example 2*3*5*7*11*13+1 = 30031, which is divisible by 59, hence NOT prime. However, what you CAN conclude is that p1*...pn+1 is either prime, or has a prime factor larger than any of the given pk's.

    17. Re:twin primes. by Ian+Glover · · Score: 1

      p1*p2*...*pn + 1 isn't necessarily prime (for example n = 4 gives 2 * 3 * 5 * 7 + 1 = 211 = 13 * 16). But if isn't then it must be divisible by prime other than p1, ..., pn so you've still got the contradiction.

    18. Re:twin primes. by miskatonic+alumnus · · Score: 1

      That is a good one --- 211 = 13 * 16 indeed. :(

    19. Re:twin primes. by miskatonic+alumnus · · Score: 1

      First, I assume you mean twin primes. Proving infinite primes is trivial and from ancient Greece. It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps). And that primes get rarer and rarer, in the limit, infinitely rare. Neither of those means that the number of primes is finite.

      They are "rare" in some senses, but not others. There are enough of them, for example, that the infinite sum of their reciprocals diverges.

    20. Re:twin primes. by isometrick · · Score: 1

      Oh my, it's modded up. Did you not notice the resolution down here mods? Sigh.

    21. Re:twin primes. by metlin · · Score: 1

      *hush* child!

      My karma would take a hit ;-)

    22. Re:twin primes. by Lifewish · · Score: 1

      If a complete list of existing primes is specified and a number is not divisible by any of these then whether we say that it is prime or has unknown prime factors is completely irrelevant as the contradiction has already been broached.

      --
      For the love of God, please learn to spell "ridiculous"!!!
    23. Re:twin primes. by miskatonic+alumnus · · Score: 1

      That is true. Nevertheless, you made the additional claim that a certain number was prime, and used that FALSE claim to arrive at your contradiction. Your proof was incomplete, so I corrected it.

    24. Re:twin primes. by jdigital · · Score: 1

      "The Music of The Primes" by Marcus du Sautoy, Harper Collings 2004.
      http://www.amazon.com/exec/obidos/tg/detail/-/0060 935588/qid=1099578709/sr=8-3/ref=sr_8_xs_ap_i3_xgl 14/103-5861881-0888602

      Although the title sounds exactly like what you are looking for, it doesn't really talk about music made by primes. Having studied some number theory, I found the math in the book to be fairly basic - but it does give an interesting account of the history of the people involved.

      If you are interested in getting a high-level grasp of the questions involved in the distribution of prime numbers (hint: zeros of the Riemann Zeta function, perhaps http://mathworld.wolfram.com/RiemannZetaFunctionZe ros.html), then this book is worth the read - even if you have no math background.

      --
      :wq ~ ~ ~ ~ ~
    25. Re:twin primes. by ColdChrist · · Score: 1
      There is no upper bound on the maximum gap between primes. The proof is quite easy: there are (N - 1) consecutive composite numbers from (N! + 2) to (N! + N). This is because 2 divides N! + 2; 3 divides N! + 3, and so on. So if you want a billion consecutive composite numbers, such a sequence starts at (1,000,000,001! + 2).

      For those who find primes fascinating, I can recommend John Derbyshire's "Prime Obsession", a history of the Riemann Hypothesis. The math is kept to alternate chapters so it's readable as a pure history book. It does a pretty good job of explaining how Riemann's famous zeta function relates to primes. Mike

    26. Re:twin primes. by Lifewish · · Score: 1

      Yeah, the phrasing was a bit dodgy. On the other hand, it's equally dodgy to say that the number p1*p2*...*pn + 1 is the product of other primes since our assumption is that there are no other primes. Your proof and my proof are effectively equivalent, given that the contradiction kicks in before we have to decide what our "new primes" will be.

      --
      For the love of God, please learn to spell "ridiculous"!!!
    27. Re:twin primes. by Kimble · · Score: 1

      "All it proves is that there's a prime q <= p1*p2*....*p999*p1000+1"

      Minor nitpick: q isn't necessarily prime. The smallest counterexample:

      2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 = 59 * 509.

      However, it does prove that there are prime numbers larger than the last prime used to construct q, which is sufficient for the purpose of proving there are an infinite number of primes.

      --
      ..!!in an intastella burst i am back to save the universe!!
    28. Re:twin primes. by Rufus88 · · Score: 1

      There are enough of them, for example, that the infinite sum of their reciprocals diverges.

      Interesting. I'm not challenging the claim, but can you point us to the proof?

    29. Re:twin primes. by lazy_playboy · · Score: 0

      Somehow I don't think there are any directly sequential primes pairs above 2 and 3, so it seems a bit pointless naming them...

    30. Re:twin primes. by Rufus88 · · Score: 2, Insightful

      It is a proved fact that there are arbitrarily large gaps in the prime sequence (i.e. infinitely large gaps).

      Yes and no. "Arbitrarily large" is not the same thing as "infinitely large". If there were an infinitely large gap, there couldn't be a subsequent prime.

    31. Re:twin primes. by maxwell+demon · · Score: 1

      Why? After all, isn't it nice to be able to say:
      There exists an uniquely determined pair of siamese twin primes.
      BTW, there's only one golden mean as well, and it still has a name! :-)

      --
      The Tao of math: The numbers you can count are not the real numbers.
    32. Re:twin primes. by armb · · Score: 1

      Read it more carefully. Your example is correct, but not a counter example to what he actually claimed (a prime q less than or equal to p1*...).

      (Explanation - the number constructed isn't exactly divisible by any of the primes used to construct it, since it is one more than a multiple of all of them, so either it is prime itself, or it has prime factors which are larger than the "largest prime" used to construct it. So there is no "largest prime".)

      --
      rant
    33. Re:twin primes. by potifar · · Score: 1
      You can find a proof of this here for example. The idea is to use Euler's product formula for the zeta-function and the well-known fact that the harmonic series diverges.

      Interestingly enough, it is known that the sum of the reciprocals of twin primes converges (and the sum is approximately 1.90216054). Of course, if there is only finitely many twin primes, this statement is trivial.

    34. Re:twin primes. by miskatonic+alumnus · · Score: 1

      No, it is not equally dodgy. The fundamental theorem of arithmetic states that a composite number may be written (uniquely, apart from rearranging the factors) as a product of primes. Hence, the given number has a prime factor not in the list, contradicting the assumption.

      I prefer a slightly different way of looking at the proof. Claim: The list of primes is infinite. This is equivalent to claiming that for any prime p, there exists another prime p' > p. Proof: Let q be the successor of the product of all primes up through and including p. Then, if q is prime, clearly q > p. If q is not prime, then by the fundamental theorem of arithmetic, it has a prime factor p'. But, p' cannot be any of the prime factors through p. Therefore, p' > q. Q.E.D.

      In this way, we don't have a proof by contradiction.

    35. Re:twin primes. by miskatonic+alumnus · · Score: 1

      Oops! Typo before the Q.E.D. should read: p' > p.

    36. Re:twin primes. by salyavin · · Score: 1

      We are treating numerology like other -ologies. We're treating it just like scientology and astrology for example.

    37. Re:twin primes. by Anonymous Coward · · Score: 0
      Take the greek proof, where you multiply all known primes and add 1.
      Just a minor nitpick, but it isn't "all known primes," it's simply "all primes." The proof starts by assuming that there is such a thing as "all primes," and then demonstrates that this leads to a contradiction.

      The product of all known primes plus one is not necessarily prime. It depends on which primes are known and which are unknown.

    38. Re:twin primes. by isometrick · · Score: 1

      Who is "we"? I was talking about the guy in the grandparent post and his thoughts on the music of the primes and such.

      I was advising him that numerology is like astrology -- it's sometimes fun, but it is ulimately B.S.

    39. Re:twin primes. by Anonymous Coward · · Score: 0

      %s/g/sleep/coffee

      I just tried that in vi. it didn't do what i expected.

    40. Re:twin primes. by Moderatbastard · · Score: 1
      the minimum gap is actually a constant function as soon as you passed 3
      So the minumum doesn't get ever larger - an illogical construction if you think about - I was just teasing the guy.

      Actually I was thinking something similar to him, of plotting "primal separation" (difference between a prime n and the next highest one) against n just to see if it looks nice or just like noise. How would it appear with a little smoothing? On to add to the copious free time stack.
      My user ID isn't prime, but it does appear to be abundant.

      --
      1/3 of jokes get modded OT. If you get the joke, mod 1 in 3 insightful/interesting/underrated to restore karma balance.
    41. Re:twin primes. by JuggleGeek · · Score: 1
      The actual proof that there are infinite primes is more complex. But here's a simplified version which I stole word for word from from Harald Tveit Alvestrand.

      ASSUME that the number of primes is finite.

      THEN IN THEORY, one could list them all, forming "the set of all primes". Then, we can multiply them together, and add 1 to the result.

      The resulting number is obviously (by rules of mathematics):
      - Not any of the known primes, since it is larger than them all
      - Not divisible by any of the known primes, since it is 1 larger than their product

      THEREFORE, it is either a prime number which is not a known prime or a product of primes that are not in the set of all known primes.

      This is inconsistent with our assumption, which we started with.

      THEREFORE, we have proved a negative: The statement "The number of primes is finite" is false.

    42. Re:twin primes. by curtlewis · · Score: 1

      except that if you add 1 to a prime, it's divisible by 2 and therefore, not a prime.

    43. Re:twin primes. by cburley · · Score: 1
      except that if you add 1 to a prime, it's divisible by 2 and therefore, not a prime.

      But the proof adds 1 to the product of all known primes.

      E.g. 2 * 3 + 1 => 7, which is a prime.

      2 * 3 * 5 + 1 => 31, which is a prime.

      2 * 3 * 5 * 7 + 1 => 211, which is either a prime or a product of primes larger than 7.

      And so on.

      --
      Practice random senselessness and act kind of beautiful.
    44. Re:twin primes. by JuggleGeek · · Score: 1
      Assume that the only known prime numbers are 2, 3, 5.

      The product of all primes would be 30. Add 1 to the product, you have 31.

      According to the basic "proof" (it's not really a proof, as written) then 31 would be either a new (previously unknown) prime, or a product of primes that are not yet known.

      From the "proof":
      THEREFORE, it is either a prime number which is not a known prime or a product of primes that are not in the set of all known primes

      In my example, 31, we have found a prime number. In order to prove that the new number is prime, you would have to factor it.

      In all cases, the number you end up with is going to either be prime, or if not prime, then factoring that number should teach you about a prime number you hadn't previously known about.

      Following our example, we now know about 2, 3, 5, and 31. Those are our "known primes". We run the test again. 2 * 3 * 4 * 31 = 930, and then we add 1 to the product of all known primes. So either 931 is a prime number, or it can be factored by a prime number which isn't in our list of known primes.

      In this case 931 isn't prime. When you try to factor it to prove that it is prime, you are going to find a factor which is a prime number, and is not in our set of known prime numbers. Thus the set of known prime numbers grows, either way. And so, we've proven that there must be an infinite number of prime numbers.

    45. Re:twin primes. by Ian+Glover · · Score: 1

      Ah well, that'll teach me to run bc without setting the scale (and not turning my brain on enough to realise a multiple is probably even! :-).

      But how about 2 * 3 * 5 * 7 * 11 * 13 = 30030 and 30031 = 59 * 509. I think that's right. (Famous last words?)

  9. The Real Twin-Prime Proof by bearnol · · Score: 3, Informative

    http://www.bearnol.pwp.blueyonder.co.uk/Math/wanle ss2.html

    1. Re:The Real Twin-Prime Proof by carnivore302 · · Score: 1

      While I'm not a mathematician, I'm sure this proof is flawed because of the way it works with infinite series.

      It kind of reminds me of the "proof" that 0 equals 1.

      --
      Please login to access my lawn
    2. Re:The Real Twin-Prime Proof by metlin · · Score: 1

      Wow. That site seems to have a lot of other cool stuff, too. Thanks!

      I'm guessing you're probably not the same James Wanless as the tarot reader/whatever?

    3. Re:The Real Twin-Prime Proof by bearnol · · Score: 1

      Assuming your first comment is meant without sarcasm (of which I have encountered quite a lot :-( ) - thank you too - I hope you do indeed find my site of interest...
      Wrt your second comment - that is correct - he and I are separate individuals, with no direct connection other than our names - though I do quite like tarot! :-)

    4. Re:The Real Twin-Prime Proof by metlin · · Score: 1

      No sarcasm intended, merely meant it as a compliment. Noticed that the upper directory had a lot of other cool math stuff, too.

      (haven't gone through them - yet, merely noticed that there seemed to be a lot of good mathematical content).

      You should probably read Primes is in P - good paper.

      PS - There is no such thing as FBT, atleast AFAIK. Is that one of yours? Has it been published/peer reviewed?

    5. Re:The Real Twin-Prime Proof by metlin · · Score: 1

      ROTFL!

      Didn't realize for a fact about some of the stuff you have, nice :-P

      Almost had me, until I decided to look deeper.

    6. Re:The Real Twin-Prime Proof by krymsin01 · · Score: 1

      It can, for large values of 0.

      --
      stuff
    7. Re:The Real Twin-Prime Proof by bearnol · · Score: 1

      Yes, indeed - the funny thing is (and it's a REALLY big joke! :-) it actually _is_ all true and complete ie correct...
      J

    8. Re:The Real Twin-Prime Proof by metlin · · Score: 0

      Ofcourse.

      Proof by induction, eh mate? ;-)

      Wonder how many math-challenged would actually get it, though. Good one!

    9. Re:The Real Twin-Prime Proof by Anonymous Coward · · Score: 0

      You actually think that's a valid proof?

      Sheesh. Wanless is a well-known crank. You'd do better to spend your time studying real stuff instead of his delusional ravings.

    10. Re:The Real Twin-Prime Proof by metlin · · Score: 1

      I'd say he's more of a troll, than a crank :-)

      A class AST troll (and I actually fell for it, sheesh). Didn't bother reading through - realized what it was once I did.

      Oh well.

    11. Re:The Real Twin-Prime Proof by potifar · · Score: 1

      +4 Informative???? That page contains no information whatsoever. Plenty of nonsense though.

    12. Re:The Real Twin-Prime Proof by abiessu · · Score: 1

      I think the parent should be "+5, funny"... the text of Wanless' Theorem is below.

      ---
      WANLESS' THEOREM

      There exist an infinite number of pairs of primes, P and Q, s.t. P-Q=2N, for all N
      (Corollaries include affirmation of the Twin Prime Conjecture)

      Proof:
      Let p0,p1,p2... be the positive primes, including 1, in inceasing order.

      ** first off, 1 is not prime... *sigh*

      Let Pn=p0p1p2...p(i0-1)p(i0+1)...p(i1-1)p(i1+1)...pn + (p(i0)**j0)(p(i1)**j1)... and
      let Qn=p0p1p2...p(i0-1)p(i0+1)...p(i1-1)p(i1+1)...pn - (p(i0)**j0)(p(i1)**j1)... [any i, j]

      ** any i, j? how about i = pi and j = e?

      Note that hcf (Pn, p0p1p2p3p4...pn) = 1 and hcf (Qn, p0p1p2p3p4...pn) = 1 [Euclid]

      ** what does hcf stand for?

      Then Pn and Qn are either both prime or
      Pn is divisible by a prime greater than pn or
      Qn is divisible by a prime greater than pn

      ** how, exactly, are Pn and Qn related? oh, and why are we restricted to these three outcomes?

      Let n->99999...
      ** unfamiliar notation...

      => pn->99999... [Euclid]
      ** unfamiliar theorem

      => Pn and Qn are both prime
      ** where was this shown? (as opposed to being simply stated)

      => There exist an infinite number of pairs of primes, Pn and Qn, s.t. Pn-Qn=2N [any N>=0] (1)
      ** true enough, as true as there are an infinite number of primes...

      => There exist an infinite number of pairs of primes, Qn and Pn, s.t. Qn-Pn=2N [any N There exist an infinite number of pairs of primes, P and Q, s.t. P-Q=2N [any N] (3)

      ** this statement is true, and an echo (possibly to avoid the use of absolute value symbols or other such paraphernalia). unfortunately, it is not the truth the author is after. the desired outcome is to be able to say "for all N, Qn-Pn = 2N has an infinite number of solutions for primes Qn, Pn"; rather, we have arrived with "Qn-Pn = 2N has an infinite number of solutions for primes Qn, Pn, for all N". the one case is quite restrictive, the other, not much.

      Corollary (Twin Prime Conjecture):
      (3) [N=1]

      ** see immediately previous comment. just because there are infinite primes (what the statement before this one says, in effect) does not mean that for any particular N, there are an infinite number of pairs of primes whose absolute difference is N.

      Copyright 1997 James Wanless
      ---

      Here's a neat little theorem to describe *all* numbers >1 which are not prime:

      k+1 is not prime iff there exist a, b in the positive integers such that k = a*b+a+b

      It is a semi-trivial exercise to come up with a similar equation to represent all non-twin-prime pairs. Not that I've been working on it for the last four years or so. :-P IMO, either this or some analytic method are our only ways of really tackling this problem.

      (Note that, of course, once you have everything that is not prime, it's pretty easy to pick out those things that are.)

      --
      Let S_n = {nst+us+vt : s,t in Z \ {0}, u,v in {-1,1}}. For all n in Z where |n| > 2, Z \ S_n is infinite... right?
    13. Re:The Real Twin-Prime Proof by Anonymous Coward · · Score: 0

      Well, here's your mistake:

      "Let n->99999...
      => pn->99999... [Euclid]
      => Pn and Qn are both prime"

      That doesn't show that Pn and Qn are prime, at all. Just because pn goes to infinity doesn't mean it can't divide Pn. It can definitely be the case that px n. For example, as x -> infinity x^2 -> infinity and x^4 -> infinity, but x^2 still divides x^4.

    14. Re:The Real Twin-Prime Proof by fatphil · · Score: 1

      James Wanless is a known sci.math loon, and can be safely ignored without missing anything of merit.

      I'm sure there's plenty of case history on googlegroups.
      Oooh, I joust noticed that a googlegroups search for:
      "James Wanless" idiot
      brings up one of my posts as the top hit!

      FP.

      --
      Also FatPhil on SoylentNews, id 863
    15. Re:The Real Twin-Prime Proof by Anonymous Coward · · Score: 0

      Oh, bollocks. I was completely taken in! Oh well, I'm kind of relieved it's not a serious "proof"...

    16. Re:The Real Twin-Prime Proof by bearnol · · Score: 1

      Who won the World Series this year?! :-)

  10. Re:FROST PIST by metlin · · Score: 0, Offtopic

    You must be a pure mathematician.

    You seem quite cut off from the reality of a first post. ;-)

  11. Re:Not quite ready for prime time by Anonymous Coward · · Score: 5, Insightful

    Umm.... cryptography? You ever use SSL?

  12. Poor hyperlinking by BarryNorton · · Score: 2, Insightful

    While Slashdot stories (unlike most of the Flash-based web) can be a good example of hyperlinking, this story (after the first link) was appalling - why was the link to the withdrawal placed around the words 'infinitiely many twin primes'? Not only did I immediately wonder why there seemed to be no link to evidence of the withdrawal, but there was no direct link to explain what the twin prime conjecture is...

  13. Serious Error.. by D-Cypell · · Score: 3, Funny

    [i]it seems that a hole has recently been found in the proof[/i]

    He forgot to carry the 1

  14. Way to keep on top of things! by HiLander4237 · · Score: 2, Interesting

    News that's only 5 months out-of-date.

  15. Math humor by Brian+Kendig · · Score: 3, Funny

    At a conference, a mathematician proves a theorem. Someone in the audience interrupts him: "That proof must be wrong. I have a counterexample to your theorem." The speaker replies, "I don't care, I have another proof for it."

    1. Re:Math humor by Anonymous Coward · · Score: 1, Funny

      And here's how to confuse a mathematician:

      Let odds be even...

    2. Re:Math humor by julesh · · Score: 1

      You, my friend, must be a mathematician, because only a mathematician would say that "you can prove anything from a contradiction". You are clearly confused, seeing as you don't see how this statement would confuse a mathematician. It seems to work...

  16. Please don't start... by Lifewish · · Score: 5, Funny

    An example of the maths humour genre from my Director of Studies (who was pissed at the time):

    An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

    "How interesting," observed the astronomer, "all scottish sheep are black!"

    To which the physicist responded, "No, no! Some Scottish sheep are black!"

    The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

    Upon which the others chorused "Shut up you ****ing pedant!" and hurled him out the train window. ...it seemed funnier at the time. Specially after the Zorb's Lemon joke.

    --
    For the love of God, please learn to spell "ridiculous"!!!
    1. Re:Please don't start... by RichDice · · Score: 2, Funny
      Here's the joke that completely killed me and my friends doing physics & astronomy degress back just a tad more than a decade ago...

      There once was a very wealthy man who enjoyed greatly betting on horse races. As he was motivated to win in all his endeavours, he desired to find a perfect method for placing his bets at the track.

      To this end, he hired three experts whom he set upon the task of finding a perfect betting system. They were a biologist, a statistician, and a physicist. He gave them a year to investigate and told them to present their results after the year was up.

      When it was time to present the results, he gathered them together.

      "Did you find a perfect system?" he asked the biologist. "I studied everything I could about the muscular power, reflex reaction time, diet, training, and many other things. Unfortunately the variables were just too complicated and there were too many of them, so I couldn't find a perfect system."

      Not a problem, thought the man, I have two other experts. So he asked the statistician if he had found a perfect system.

      "I analyzed every piece of data that I could: track condition, weather conditions, time of day, jockey, competitors, age of the horse... just everything. I ran every regression I could. But there were just too many variables and I couldn't develop a predicable model from them."

      Now the man was concerned, so with hestitation he asked the physicist if he had discovered a perfect system for betting on horses at the race.

      "Yes!" exclaimed the physicist, "I have!"

      "Terrific!" said the man.

      "Well," started the physicist slowly, "there is one problem. It only works for spherical horses moving through a vacuum."

      Cheers,
      Richard

    2. Re:Please don't start... by schotty · · Score: 1

      That is funny, since I know where the joke is coming from.

      --
      Sigs are nice guns ...
    3. Re:Please don't start... by Mercuria · · Score: 1

      A mathemetician, a physicist and an engineer were asked to find the volume of a red rubber bouncy ball. the mathemetician measured the circumference and computed the volum using the formula. The physisist dropped it in a glass of water and measured the displacement. The engineer looked up the red rubber ball's serial number in the Red Rubber Bouncy Ball Specifications manual.

    4. Re:Please don't start... by JuggleGeek · · Score: 1
      Math jokes, huh? Ok, I'm game.

      A few days ago, I ran into an old friend of mine. He's a mathemetician, and taught me a lot about programming when I was learning. We chatted for a few minutes, and as we were parting ways, he called "Have a Merry Christmas!". I told him "You're jumping the gun - tomorrow is Halloween."

      He replied "I always get those mixed up, because OCT 31 = DEC 25."

  17. Treat any -ology the same? by Anonymous Coward · · Score: 0, Insightful

    Is this intended to be a positive or negative treatment of -ology words in general.

    Either way it is silly. We have:

    Numerology

    Geology

    Astrology

    Zoology

    Scientology

    Psycology

    Phrenology

    Biology

    Theology

    Anaesthesiology

    Do you really advocate treating all these the same?

    1. Re:Treat any -ology the same? by isometrick · · Score: 1

      I thought about that when I was writing it, but I thought that most people would get the meaning of what I was saying.

      I guess I overestimated.

  18. Re:Lemma by Anonymous Coward · · Score: 0

    (The exception being the pair 3,5.)

  19. proffered paired prime proof poofed by dominux · · Score: 2, Funny

    proffered paired prime proof postulated pants

    1. Re:proffered paired prime proof poofed by HMA2000 · · Score: 4, Funny

      Previously Proffered Paired Prime Proof Pwn3d!

    2. Re:proffered paired prime proof poofed by antoy · · Score: 1

      Wish I had mod points.

  20. Well, you know what they say... by Lifewish · · Score: 1

    Engineers think that equations imitate reality
    Physicists think that reality imitates equations
    Mathematicians can't make the connection

    --
    For the love of God, please learn to spell "ridiculous"!!!
    1. Re:Well, you know what they say... by Anonymous Coward · · Score: 0

      An engineer and a mathematician both approached a woman asymptotically. The mathematician never touched her, but the engineer got close enough for all practical purposes.

  21. Hole found in first psots? by ArsenneLupin · · Score: 1
    Continuing on a previous slashdot story regarding Arenstorf's proof of the existence of Infinitely Many First Posts, it seems that a hole has recently been found in the proof,

    Are you thinking about the same hole that I am thinking about?

    1. Re:Hole found in first psots? by Anonymous Coward · · Score: 0

      "Are you thinking about the same hole that I am thinking about?"

      Yes, your mom is hot, isn't she?

  22. Develop secure web applications just using Excel by ArsenneLupin · · Score: 1
    Develop secure web applications just using Excel. [jedox.com]

    But your site uses PHP... Hmm, does that mean there is no way of making a truly secure web application using only true Micro$oft technologies such as ASP and SQL server?

  23. Correcting 'proof'? by Rirath.com · · Score: 4, Funny

    "however mathematicians remain hopeful that the proof can be corrected."

    Sounds a lot like Republicans.

    1. Re:Correcting 'proof'? by l2718 · · Score: 1

      "however mathematicians remain hopeful that the proof can be corrected."

      Actually, nearly all number theorists don't believe there's any hope of correcting this proof. It's highly unlikely that clever manipulation of the exponential sums would suffice.

      The problem is that we don't know how to distinguish two primes from three. In the 60s Chen showed that there exist infinitely many pairs p,p+2 such that p+2 is a product of 2 primes (and similarly that every even number is a sum of a prime and a product of two primes).

      The preprint does not claim any new idea. It doesn't even refer to this essential obstruction (the 'parity problem') everyone else encounters, while supposedly circumventing it.

  24. Good thing we are all really nerds here by Hao+Wu · · Score: 3, Insightful

    Luckily since we are all true "geeks" here at Slashdot, we can understand this math as we read through it. It's not like we're all posers who are really only interested in trendy politics, media, and video games.

    --
    I suggest you read Slashdot
  25. And still... by Wig · · Score: 1

    ...I have absolutely no clue what any of this means.

  26. Re:My Twin Prime problems by gardyloo · · Score: 1

    Best of luck on the proposal!

    You really should move to The Twin Cities. Surely that cold clime would solve the twin prime problem...

  27. Re:Develop secure web applications just using Exce by charliesmagic · · Score: 1

    Arsenne... No, ASP & SQL Server work fine. But they won't compile excel worksheets into secure multi-user web pages. You have to code everyhing. But excel users can use this to do the same thing without knowing any code. It's compiled into PHP, etc for them in the background. It's for business users, spreadsheet jockeys, who don't need to know ASP or even PHP. But we're straying from my witty remark about the twin primes topic....

    --

    Charlie's Magic

  28. Re:Lemma by Anonymous Coward · · Score: 0

    so easy. All primes are congruent to +- 1 mod 6, so n must be congruent to -1 mod 6 (otherwise n+2 would be congruent to 3 mod 6, contradiction), so n+1 is divisible by 6. Give us a HARD problem!

  29. Re:Not quite ready for prime time by stud9920 · · Score: 0

    alabama pi

  30. infinite primes troublesome by hipparchus · · Score: 1

    to me the existence of infinite primes seems obvious.
    Some people find inifinity troublesome.

    1. Re:infinite primes troublesome by hipparchus · · Score: 1

      and infinity even harder

  31. TWINS by torrents · · Score: 1

    who here wouldn't like to have a pair of prime twins...

    --
    Get your torrents...
  32. She said yes! by purduephotog · · Score: 1

    WhooooooHooooo!

    http://www.gotSheep.com/EMK

    Thanks for the good luck ;)