Prime Numbers Not So Random?

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Posted by chrisd on Monday March 24, 2003 @07:58PM from the voltron-under-control dept.

Jeff Moriarty writes "Some physicists believe they might have caught a whiff of a pattern in the sequence of prime numbers. This would have a huge impact across mathematics, and to people who just really like primes... or like being Prime."

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Immicibility gap by October_30th · 2003-03-24 20:02 · Score: 0, Flamebait

Physicists and mathematicians don't mix.

--
The owls are not what they seem
1. Re:Immicibility gap by diryn · 2003-03-24 20:03 · Score: 0
  
  Bah, can't even get at the site.. and I saw it first!
  
  --
  Reductio Ad Adsurdium David
2. Re:Immicibility gap by Anonymous Coward · 2003-03-24 21:12 · Score: 2, Funny
  
  You sir, are a liar. Physicists mix quite well.
anyone else getting the feeling... by ddd2k · 2003-03-24 20:08 · Score: 4, Interesting

the interval thing seemed like such a trivial observation. surely many others have easily noticed that. Its another "I think i discovered a pattern" claim, while still have no way to prove it.

--

Great Atrocit
1. Re:anyone else getting the feeling... by Ieshan · 2003-03-24 20:16 · Score: 1, Funny
  
  In Mathematics, there's nothing that's "proven" that isn't explicitly defined as such. Notice how the Pythagorean Theorem is just that - a Theorem, not 'The Pythagorean Law'.
  
  The reason - it's impossible to prove anything on an infinite set of data that isn't defined in the parameters of the data set.
  
  A Theorem is a tested hypothesis, and these guys aren't even offering this. They're simply saying, "Look, we found an interesting pattern." As someone who's hopefully a future scientist, I'd say this is noteworthy - some scientists in the community noticed something interesting and submitted it so lots of other scientists could attempt to validate the claim.
  
  It's not *trivial*, if it was, why hasn't it been done before?
2. Re:anyone else getting the feeling... by ddd2k · 2003-03-24 20:25 · Score: 2, Insightful
  
  The reason - it's impossible to prove anything on an infinite set of data that isn't defined in the parameters of the data set.
  This is not physics, in math u can easily prove theories involving infite data sets. Hello? irrational numbers? infitie series? they were all logically proven. Its *NOT* noteworthy because anyone can come up with these observations, but it takes a genius to prove it.
  
  --
  
  Great Atrocit
3. Re:anyone else getting the feeling... by Ieshan · 2003-03-24 20:34 · Score: 1, Insightful
  
  There, you've done it.
  
  You've "easily" proven things by defining them as something. An irrational number is a number with no known, infinite, repeatable sequence? You've *defined* it that way, that doesn't mean you've ever *proven* a number irrational.
  
  People are still doing work on Pi to see if it's got repeatable, discernable patterns someplace. The application of Logic does not prove things, proof cannot be generated with interpolation/extrapolation. In the scientific community, proof is established by repeated experimental repetition, in Mathematics, testing this theory lots of times with lots of different numbers (see computers). A Geometry proof, for instance, is an elegant placement of existing theorems to define a new one. "A works and B works and C works, therefore, D works." A Geometry *theorem* or *testable observation* is the creation of a new foundation that can be built from.
  
  Of course they're noteworthy. Who are you to say that the editors of Nature don't know what to publish?
4. Re:anyone else getting the feeling... by farnsworth · 2003-03-24 20:35 · Score: 2, Funny
  
  This is not physics, in math u can easily prove theories involving infite data sets. Hello?
  In English, you can easily use real grammar and real words. On slashdot, however, you are on your own.
  
  --
  There aint no pancake so thin it doesn't have two sides.
5. Re:anyone else getting the feeling... by ddd2k · 2003-03-24 20:41 · Score: 1
  
  in Mathematics, testing this theory lots of times with lots of different numbers (see computers).
  are you insane? of course PI wasn't proven, but haven't you ever heard of proves for irrational numbers such as root 2? Appearantly you've never heard of infinite series proves either... maybe short of understanding in calculus?
  
  --
  
  Great Atrocit
6. Re:anyone else getting the feeling... by WatertonMan · 2003-03-24 20:45 · Score: 1, Interesting
  
  While traditionally there has been a wide gap between physics and mathematics in terms of method, quite a few philosophers have argued that this gap has been closing. One big reason for it is the advent of the computer. Many of the most famous mathematical discoveries of the last decade have involved a *lot* of computer work. To such an extent that suggesting that anyone has actually gone through every step of the proof is likely wrong. Further studies in fields like chaos have tended to use computers like a laboratory, utilizing a lot of the methadology of physics.
  One good paper on this phenomena of how proof has changed in math is William Thurston's, "On Proof and Progress in Mathematics." A great book that goes through a lot of recent work in philosophy of mathematics is New Directions in the Philosophy of Mathematics
  by the Princeton University Press. While I still am primarily a Constructivist, I find that recent anti-foundationalist approaches to mathematics are very interesting. In particular you might find Putnam's assertion that math is becoming quasi-empirical very interesting.
  I always find Putnam interesting, even though I often disagree with him. He tends to try to blur the realist - anti-realist distinction in ways that end up being more slight of hand. (IMO)
  Anyway, I think that you are adopting a foundational view of mathematics for which there are good reasons to reject. Further we can have a good reason for thinking a theorem correct without necessarily being able to prove it from strict foundations. And indeed the crisis in mathematical foundations at the end of the 19th century was the recognition that math had been proceeding without doing what you suggest. That was partially the impetitus behind such things as Whitehead and Russell's work on mathematical foundations.
7. Re:anyone else getting the feeling... by Ieshan · 2003-03-24 20:49 · Score: 1
  
  Right, which is why I was saying the finding was noteworthy and significant instead of shooting it down simply because they haven't "proven" anything. =P
8. Re:anyone else getting the feeling... by itsme1234 · 2003-03-24 21:09 · Score: 1
  
  Look, Pi is _irrational_. The proof is not trivial, but it's clear. Pi is not even algebraic (this is proved, also).
9. Re:anyone else getting the feeling... by itsme1234 · 2003-03-24 21:20 · Score: 1
  
  The Pythagorean Theorem is a Theorem because it fits the definition for the Theorem, not because some stupid reason about infinity. A theorem is a logical assertion which can be proved using (=it is implied) by the axioms (statements which are given to be true).
10. Re:anyone else getting the feeling... by Yokaze · 2003-03-24 21:29 · Score: 3, Insightful
  
  > In the scientific community, proof is established by repeated experimental repetition, in Mathematics, testing this theory lots of times with lots of different numbers (see computers)
  
  Sorry. Say that to a mathematician, and see how he laughs at you, or kicks you out.
  
  A theorem is statement which can be verified by mathematical operations.
  
  The statements usually includes axioms, which are not provable, and which define the mathematical operations on the given problem. The only thing you have to do is show is, given these axioms, the statement is always true.
  
  The sequence of application of axioms is called "proof".
  
  And mathematicians are very peculiar with "always". For scientists "always" means "many times, and until some shows otherwise", because you can't define these axioms.
  
  Mathematics is not the kind of science you are thinking of. You are thinking of natural science.
  In mathematics, humans define the axioms. They may, or may not bear any relationship to reality.
  It some aspects, it resembles more philosophy than physics.
  
  > Who are you to say that the editors of Nature don't know what to publish?
  
  Probably a mathematician. They don't give a lot on physicists saying, "Hey, by finding some statistical correlation, we found a pattern, which holds true, in our finite data set, most of the time".
  
  --
  "Between strong and weak, between rich and poor [...], it is freedom which oppresses and the law which sets free"
11. Re:anyone else getting the feeling... by Scarblac · 2003-03-24 21:30 · Score: 2, Insightful
  
  In Mathematics, there's nothing that's "proven" that isn't explicitly defined as such. Notice how the Pythagorean Theorem is just that - a Theorem, not 'The Pythagorean Law'.
  
  I don't see any difference between a "law" and a "theorem".
  
  Anyway, a theorem is a formula that can be proven true.
  
  Formulas that aren't theorems are, well, just formulas.
  
  All the math we know consists of theorems, things that have been proven true. There are also some so-called "conjectures" - that means "we think this is a theorem but haven't found the proof yet.".
  
  Experiments, hypotheses, data, tests, all that belongs to science - and math is not science.
  
  --
  I believe posters are recognized by their sig. So I made one.
12. Re:anyone else getting the feeling... by Scarblac · 2003-03-24 21:36 · Score: 3, Informative
  
  You've "easily" proven things by defining them as something. An irrational number is a number with no known, infinite, repeatable sequence? You've *defined* it that way, that doesn't mean you've ever *proven* a number irrational.
  
  Proof that the square root of 2 is irrational: http://everything2.com/index.pl?node_id=928307
  
  Proof that e is irrational: http://everything2.com/index.pl?node_id=930313
  
  Better examples are obviously out there, but I just searched for 'irrational' on E2... You're very ignorant.
  
  --
  I believe posters are recognized by their sig. So I made one.
13. Re:anyone else getting the feeling... by Yokaze · 2003-03-24 21:40 · Score: 1
  
  Sorry, a minor correction:
  
  > The sequence of application of axioms is called "proof".
  
  The sequence of application of mathematical operations, as defined per axioms, which reduces the statement to an axiom is called "proof".
  
  --
  "Between strong and weak, between rich and poor [...], it is freedom which oppresses and the law which sets free"
14. Re:anyone else getting the feeling... by KDan · 2003-03-24 22:45 · Score: 2, Informative
  
  Sorry dude, you're wrong.
  
  In the scientific community, proof is established by repeated experimental repetition, in Mathematics, testing this theory lots of times with lots of different numbers (see computers).
  
  Apparently you've just started your degree (or maybe not even yet) so you haven't heard of proof by induction. In proof by induction, you prove that if a statement is true for q=n, it is also true for q=n+1. That's step 1. Then you go and prove that it's true for q=1. Once you've done those two steps the statement is proven for all integer values of q.
  
  Daniel
  
  --
  Carpe Diem
15. Re:anyone else getting the feeling... by taliver · 2003-03-24 23:55 · Score: 1
  
  Notice how the Pythagorean Theorem...
  
  Like this?.
  
  Took about 30 seconds with google, and that's because I misspelled Pythagorean. Good thread, however.
  
  --
  
  I demand a million helicopters and a DOLLAR!
16. Re:anyone else getting the feeling... by Smidge204 · 2003-03-25 00:27 · Score: 4, Funny
  
  Proof: All odd numbers are prime.
  
  Mathematitian: "1 is prime, 3 is prime, 5 is prime, 7 is prime. The rest are prime by induction."
  
  Physisist: "1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is not but is likely to be experimental error, 11 is prime, 13 is prime..."
  
  Engineer: ""1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime to a reasonable degree of accuracy, 11 is prime, 13 is prime..."
  
  Computer Scientist: "1 is prime, 1 is prime, 1 is prime, 1 is prime..."
  
  </joke>
  =Smidge=
17. Re:anyone else getting the feeling... by ConceptJunkie · 2003-03-25 01:43 · Score: 1
  
  I agree. This doesn't sound like anything different from all the patterns (real or not) discovered by this writer playing with his TI-30 while bored in math class.
  
  Of course, the article was sparse on details, but it seems they are taking a physical sciences approach to mathematics... make a hypothesis and experiment to see if it is correct. In math, this is useless because as a system of logic, mathematical proofs can be either proven or disproven 100% (Godel exceptions notwithstanding). That never happens in the physical world.
  
  --
  You are in a maze of twisty little passages, all alike.
18. Re:anyone else getting the feeling... by MarvinMouse · 2003-03-25 01:43 · Score: 1
  
  Well, it's a well proven fact in mathematics that given enough random points on a graph, patterns have to emerge.
  
  I don't remember the exact name of the theorem, but Erdös, and his contemporaries were main figures in the development of it.
  
  Given a billion prime numbers, you have essentially a billion points on a graph, naturally meaningless patterns are going to emerge. It doesn't really tell you anything though.
  
  --
  ~ kjrose
19. Re:anyone else getting the feeling... by Tom7 · 2003-03-25 03:50 · Score: 1
  
  1 isn't prime.
20. Re:anyone else getting the feeling... by Guignol · 2003-03-25 04:19 · Score: 1
  
  Unfortunately, not everything in math can be a theorem.
  We know since Gödel that some truthes are just "truthes", like mere accidents, which means, they cannot be proven with our set of axioms.
  For this precise reason, the mathematics universe is starting to look a lot more like the physicis universe, in that laws might be an option to consider.
  Say we discover an appearant pattern in prime numbers distribution. Maybe this pattern, experimentaly found has no way to be proven.
  The real bad news is, if it is one of those unprovable nightmares, we won't know it until the end of times :) there is no way to be sure.
  Then maybe if strong 'experimental' evidence is given, maybe this conjecture can slowly become a law, as it works in physics, allowing a (new ?) branch of experimental mathematics to progress faster based on experimental evidence.
21. Re:anyone else getting the feeling... by aaarrrgggh · 2003-03-25 04:44 · Score: 1
  
  What about 2?
22. Re:anyone else getting the feeling... by Froze · 2003-03-25 04:51 · Score: 1
  
  Don't you mean 10? ;-)
  
  --
  -- The morphemes of your disquisition are ascertainable, but they have eschewed an ambit of transpicuous exposition.
23. Re:anyone else getting the feeling... by blonde+rser · 2003-03-25 05:58 · Score: 1
  
  Read the claim... 2 is even so the claim doesn't state anything about it.
24. Re:anyone else getting the feeling... by Scarblac · 2003-03-25 06:03 · Score: 1
  
  in that laws might be an option to consider.
  
  What are these "laws" you are talking about? Things aren't special because they have "law" in their name (for instance, in Dutch it's "Law of Pythagoras" not "Pythagoras' Theorem" - doesn't mean anything different).
  
  But ok, I cede that there are conjectures that cannot be proven and still be true. But many examples of long-lived conjectures (the "four colour theorem", "fermat's last theorem") were eventually proven. Just from looking at Gödel's constructed non-provable true statement, which was book length, I have at least a gut feeling that his Theorem shouldn't have much impact in practice.
  
  So now I'm talking about gut feelings in practice. I guess I'm defeating myself :-)
  
  --
  I believe posters are recognized by their sig. So I made one.
25. Re:anyone else getting the feeling... by 42forty-two42 · 2003-03-25 06:30 · Score: 1
  
  Obligatory karme whore: http://www.math.uchicago.edu/~wald/lit/pi_proof.tx t
26. Re:anyone else getting the feeling... by 42forty-two42 · 2003-03-25 06:32 · Score: 1
  
  Or the sequence of application of mathematical operations, as defined per axioms, which reduces the opposite of a given statement to a contradiction, is a proof.
27. Re:anyone else getting the feeling... by Anonymous Coward · 2003-03-25 06:49 · Score: 0
  
  Exactly what is it that has been "done" anyways? The article has this interesting line near the bottom:
  
  The Boston team's findings are not supported by any kind of rigorous mathematical proof.
  
  Sounds to me like they've got all the qualifications of your average /.er on this topic...
28. Re:anyone else getting the feeling... by 42forty-two42 · 2003-03-25 06:49 · Score: 1
  
  You can't prove it by induction without proving that for all odd n, if n is prime, then n+1 is prime. You just proved it for a given range.
29. Re:anyone else getting the feeling... by lylfyl · 2003-03-25 07:50 · Score: 1
  
  Art major:
  "2 is prime, 4 is prime, 6 is prime, 8 is prime..."
30. Re:anyone else getting the feeling... by Anonymous Coward · 2003-03-25 08:03 · Score: 0
  
  2 is evenly divisible only by 1 and itself, so is prime.
  
  2 is the only even prime, which is certainly an odd thing for a number to be. so, 2 is actually one of the oddest numbers around. ;-)
31. Re:anyone else getting the feeling... by Mr.+Slippery · 2003-03-25 08:13 · Score: 1
  
  it's impossible to prove anything on an infinite set of data that isn't defined in the parameters of the data set.
  
  Of course it's possible. Between high school, college, and grad school I'm sure I proved hundreds of propositions about infinite sets.
  A Theorem is a tested hypothesis, and these guys aren't even offering this.
  
  No.
  A theorem is a proven mathematical statement. E.g., the Pythagorean theorem, or the fundamental theorem of integral calculus.
  A theory is (in a scientific context) a tested and widely accepted hypothesis. E.g., the theory of relativity. In a mathematical context, a theory is a related body of study (set theory, probability theory, etcetera).
  A law is, in a scientific context, a mathematical statement of a theory - "Newton's First Law". In a mathematical context, a law is a fundamental theorem of some branch of mathematics (for example, the Law of Large Numbers).
  
  --
  Tom Swiss | the infamous tms | my blog
  You cannot wash away blood with blood
32. Re:anyone else getting the feeling... by Smidge204 · 2003-03-25 11:55 · Score: 2, Funny
  
  I suggest you upgrade your browser. Apparently it doesn't process the tag correctly.
  
  =Smidge=
33. Re:anyone else getting the feeling... by Ashen · 2003-03-25 22:19 · Score: 1
  
  There is a much simpler proof than that.
  
  Sqrt(1) Sqrt(2) Sqrt(4)
  
  1 Sqrt(2) 2
  
  In order for Sqrt(2) to be rational, it must be equal to some integer between 1 and 2. Since no such integer exists, Sqrt(2) is irrational.
34. Re:anyone else getting the feeling... by Ashen · 2003-03-25 22:21 · Score: 1
  
  stupid html...
  
  Sqrt(1) less than Sqrt(2) less than Sqrt(4)
  
  1 less than Sqrt(2) less than 2
  
  In order for Sqrt(2) to be rational, it must be equal to some integer between 1 and 2. Since no such integer exists, Sqrt(2) is irrational.
35. Re:anyone else getting the feeling... by httpamphibio.us · 2003-03-25 22:28 · Score: 1
  
  There is a difference between a proof and proving something. A proof is something which shows evidence in favor of a belief, in most cases when somebody says they have "proven" something it means that they have made something fact.
  
  --
  sig.
36. Re:anyone else getting the feeling... by stoborrobots · 2003-03-26 17:26 · Score: 1
  
  Why does your proof not show that sqrt(2) is a rational fraction between 1 and 2?
  
  --
  "Go to CNN [for a] spell-checked, fact-checked summary" -- CmdrTaco
37. Re:anyone else getting the feeling... by metlin · 2003-03-26 22:59 · Score: 1
  
  I don't see any difference between a "law" and a "theorem
  
  The reason the term law is not used is because a law is something that has to always hold true.
  
  On the other hand, a Theorem is something that is based on a set of axioms. It may change, within the limitations of the axioms or even independent of them.
  
  From a Physicist's perspective, both Newtonian mechanics and Relativistic mechanics hold true, but you do not consider relativistic mechanics for your day-to-day problems in Physics. Which is why a law holds true, immaterial of other implications, although something may supercede it, its validity is not lost.
  
  On the other hand, a theorem is built more on an observation, as a function of such laws.
  
  The laws of mathematics are the axioms. The theorems are just built on them.
38. Re:anyone else getting the feeling... by Ignominious+Cow+Herd · 2003-03-30 13:57 · Score: 1
  
  That's just it. If it is a Theorem is either is unprovable (but still quite possibly true) or just unproven so far. There are good theorems and bad ones. The good ones are either true or close enough to true that they are at least truly useful. One big example is the totality of Quantum Physics. Very useful, but most physicists would not bet you that it will ever be proved as some final Law of Physics.
  
  Laws are Theorems that have been proven true. Not just be experimentation, but by rigorous proof (Logical or Mathematic). If Fermat's last Theorem has been proven then it should be called Fermat's last Law.
  
  There's a lot of shit being posted in this story.
  
  --
  Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.
39. Re:anyone else getting the feeling... by Ignominious+Cow+Herd · 2003-03-30 14:12 · Score: 1
  
  There's a lot of shit being posted in this story ...aaand apparently I'm posting some of it. Got my definition of theorem confused with theory. Someone posted below a better/correct one. Theorems can be either proven or unproven. Laws are stipulated to be true and don't need to be proven.
  
  --
  Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.
40. Re:anyone else getting the feeling... by jc42 · 2003-03-31 03:15 · Score: 1
  
  Actually, this is the punch line to the followup to the long lists of proofs that all odd numbers are prime. The followup joke is the proof that all prime numbers are odd. This is trivial for all prime numbers but 2. For 2, the proof observes that, being even, 2 is a *very* odd prime ...
  
  --
  Those who do study history are doomed to stand helplessly by while everyone else repeats it.
41. Re:anyone else getting the feeling... by jc42 · 2003-03-31 03:21 · Score: 1
  
  I first heard the proofs that all odd numbers are prime back in the 60's, when I was in high school. There were a lot of them, for various occupations.
  
  Some of my favorites:
  
  Politician: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 11 is prime, 13 is prime; that should be enough to convince anyone.
  
  Thologian: 3 is prime; therefore all odd numbers are prime.
  
  News reporter: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime; looks like it's always true.
  
  --
  Those who do study history are doomed to stand helplessly by while everyone else repeats it.
Encryption? by asdfx · 2003-03-24 20:15 · Score: 3, Informative

I wonder if this theory could be used to produce code that could be useful for encryption based on prime numbers, such as RSA's work. Would it make it easier to produce reliable prime numbers much larger than 1024 or even 2048 bit? Further, I wonder if this could be used to drastically reduce the time required to brute force an RSA encrypted message. Could the encryption of files that were encrypted with 128 bit technology be rendered all but useless?
1. Re:Encryption? by Anonymous Coward · 2003-03-24 21:10 · Score: 0
  
  Could the encryption of files that were encrypted with 128 bit technology be rendered all but useless?
  Define "128 bit technology". It's a meaningless buzzword unless you qualify it. The gamecube is 128 bit, is it not? Does this mean that encryption does with a gamecube is inherently more powerful than encryption done with run-of-the-mill 32-bit intels?
2. Re:Encryption? by itsme1234 · 2003-03-24 21:32 · Score: 2, Insightful
  
  Uh, I fail to see why this was moderated as interesting. "128 bit technology" ? I assume you are talking about symmetrical alg., like IDEA, CAST, and many others. These are not even remotely related to prime numbers (some of them are, but not very close). And it's already simple enough to generate big prime numbers.
  Next step is to ask: "will my Diesel car become obsolete because of this theory" ?
3. Re:Encryption? by KDan · 2003-03-24 22:52 · Score: 1
  
  He was talking about RSA. And yes, if someone figures out a way to use these patterns to calculate large prime numbers more quickly, this could definitely have huge consequences on asymmetrical encryption like RSA. Depending on how much faster it makes calculation of large primes, it could either require much larger RSA keys (say 40kbit instead of 4kbit) or even make RSA and other prime-number-based encryption schemes inherently insecure.
  
  Daniel
  
  --
  Carpe Diem
4. Re:Encryption? by itsme1234 · 2003-03-25 00:57 · Score: 1
  
  RSA is "strong" not because we cannot generate prime numbers (or test if one given number is prime). In fact we can do both things VERY fast.
  
  RSA is "strong" because we cannot solve fast simple ecuations like x*y=A (where A is BIG, x,y integers). And bruteforce is NOT the fastest method available to factor integers. If it were, yes, it would help to have a faster algorithm to generate/test primes. But it's not.
5. Re:Encryption? by KDan · 2003-03-25 08:41 · Score: 1
  
  Wouldn't it be pretty fast if you start with A, put z = sqrt(A), then search around z already knowing all the prime numbers from 0 to z? If the method accelerates things enough, it's equivalent to knowing all the numbers from 0 to z. I would have thought that going through a few zillion numbers and trying to divide to see if we get an integer shouldn't take that long - at least it would take many orders of magnitude less time than trying ALL the integers in there.
  
  Oh, and from what I've seen, it does take a fair amount of time to check whether a large number is a prime. At least, if it doesn't, you need to tell Sun that their random large prime generator sucks ass as it takes more time the more certainty you need about whether the number is really a prime.
  
  Daniel
  
  --
  Carpe Diem
6. Re:Encryption? by KDan · 2003-03-25 08:44 · Score: 1
  
  I meant prime numbers from 0 to z of course.
  
  Daniel
  
  --
  Carpe Diem
7. Re:Encryption? by Anonymous Coward · 2003-03-25 22:30 · Score: 0
  
  No. That algorithm is completely worthless for factoring large integers. Consider N of 1000 bits to be factored into primes p,q each of 500 bits. Now, as an exercise, find the number of 500 bit prime numbers and think about how long it would take todo trial division with them all.
  
  Factoring is done with advanced algorithms like the Number Field Sieve in different variations and not with trial division.
8. Re:Encryption? by itsme1234 · 2003-03-26 07:11 · Score: 1
  
  The short answer is no, it won't be "pretty fast". There are just too many prime numbers between 2 and sqrt(A), if A is something like 2^1024 or 2^2048 or 2^4096 (...) to test them all.
  Right now we have better (=faster) ways to factor large integers than to bruteforce for all the prime numbers smaller than sqrt(A). Way faster.
  
  Think about it. There are about x/log x prime numbers smaller than x ! There are too many prime numbers to generate between 1 and 2^200, even if you generate one prime number in a clock cycle, no matter how fast is your computer or how many computers you have !
Cheh... but we already known it's not random by Red+Pointy+Tail · 2003-03-24 20:24 · Score: 2, Funny

We have always maintained that it is not random. In fact, our random number generator consistently generate numbers that are subsequently found to be NON-PRIME.

In our extensive (yet to be published) research, we have discovered that all PRIME NUMBERS are not just not random, but are found to have the property of NOT HAVING ANY DIVISORS APART FROM ITSELF AND 1. I've yet to verify with finding but it appears to be true with a correlation of 1.0 for all cases our research team have considered.
1. Re:Cheh... but we already known it's not random by Anonymous Coward · 2003-03-24 21:08 · Score: 0
  
  I don't know who modded this as "interesting", but you really need to get a clue. This was a joke.
  
  RNGs mostly generate non-prime numbers because the majority of numbers are non-prime.
  
  Prime numbers that don't have any divisors apart from themselves and one doesn't mean much; it's the definition of a prime number. Anybody thinking this is interesting needs to go back to high school.
2. Re:Cheh... but we already known it's not random by itsme1234 · 2003-03-24 21:13 · Score: 1
  
  Please mod the parent up, but NOT as funny. And move along, there is nothing else to see here.
3. Re:Cheh... but we already known it's not random by jsse · 2003-03-24 21:23 · Score: 1
  
  Anybody thinking this is interesting needs to go back to high school.
  
  That is a big jump for him/her! Consider this moderator obviously comes from elementary grade. :)
4. Re:Cheh... but we already known it's not random by nathanh · 2003-03-24 22:57 · Score: 1
  
  The funniest part of this post is that it got moderated "insightful". Hahaha.
figure & ground by obtuse · 2003-03-24 20:46 · Score: 3, Interesting

Yeah, I remember being excited when I saw a graph of primes that were dots in a field of blank composites. There were lines & patterns all over the place. Wow!

Then I realized that the composite numbers will each make a pattern in any graph. By their nature they repeat.

What I was looking at was the space in between the patterns created by the composites. For example, all primes are odd. There's a set of straight lines on any graph. Well, it's more enlightening to say that none are even, becasue then they'd be divisible by two. Each new set of composites creates another pattern that makes a hole in possible primes.

--
Assembly is the reverse of disassembly.
1. Re:figure & ground by Anonymous Coward · 2003-03-24 22:37 · Score: 1
  
  For example, all primes are odd.
  Uh, hello? 2?
2. Re:figure & ground by Scarblac · 2003-03-24 23:08 · Score: 1
  
  For example, all primes are odd.
  
  Uh, hello? 2?
  
  That's just a measuring error :-)
  
  --
  I believe posters are recognized by their sig. So I made one.
3. Re:figure & ground by unitron · 2003-03-24 23:50 · Score: 1
  
  2 is the oddest prime number of all, 'cause it doesn't obey the rule all the others do of not being divisible by 2.
  Yeah, I know. Terrible pun. So, if anybody ever figures out how to define division by zero, will this screw up the definition of a prime number?
  
  --
  I see even classic Slashdot is now pretty much unusable on dial up anymore.
4. Re:figure & ground by DjReagan · 2003-03-25 01:14 · Score: 1
  
  Uh, it *is* divisible by two. 2/2=1
  
  --
  "When I grow up, I want to be a weirdo"
5. Re:figure & ground by unitron · 2003-03-25 01:45 · Score: 1
  
  And because it is divisible by 2, it does not follow the rule followed by all other prime numbers of *not* being divisible by 2, hence making it an "odd" prime number in spite of being "even". You read my previous post too quickly, apparently.
  
  --
  I see even classic Slashdot is now pretty much unusable on dial up anymore.
6. Re:figure & ground by Anonymous Coward · 2003-03-25 06:47 · Score: 0
  
  There is nothing particularly strange about 2 being a prime. It's just that we have a special word for numbers that divide by 2. Invent another special word (= treven) for numbers that are divisible by three - what happens? Wow - isn't 3 strange - the only prime number that is treven. Repeat this for as long as it takes to sink in....
7. Re:figure & ground by unitron · 2003-03-25 08:09 · Score: 1
  
  You're unfamiliar with the concept of "puns", aren't you?
  Unless you're not seeing the posts to which I've been replying.
  
  --
  I see even classic Slashdot is now pretty much unusable on dial up anymore.
8. Re:figure & ground by JDWTopGuy · 2003-03-25 13:38 · Score: 1
  
  Excuse my extreme naivete, but if division is measuring how many times you can take one number from another, wouldn't dividing anything by zero give you infiniti?
  
  IE: 4 / 2 = 2 because you can remove 2 twice from 4 before you get a number less than 2 (0).
  
  So then, since removing 0 from anything has no effect, you can do it an infinite number of times with no change, right? (Kinda like a geek asking a babe for a date... heh)
  
  --
  Ron Paul 2012
9. Re:figure & ground by unitron · 2003-03-25 21:45 · Score: 1
  
  I like the other guy's positive and negative infinity explanation but the way I explain it to myself is that zero isn't just the abscence of something, it's actually nothing, and anything that's something doesn't have any nothings in it to remove, although I admit that even that explanation falls apart when you consider 0/0. (It seems to me that zero should go into zero exactly one times, but I'm sure there must be one of those chain of equations that starts there and ends with 2=3 or something like that.)
  
  --
  I see even classic Slashdot is now pretty much unusable on dial up anymore.
10. Re:figure & ground by fuctape · 2003-03-30 06:07 · Score: 1
  
  I think you're talking about this. It shows the spiral construction you can make with primes and lets you set your own parameters. Also, it makes clear that 2 is prime because its only divisors are 1 and itself, the definition of prime. So 2 is *not* a weird prime because it's divisible by 2.
Physicists pulling a cold fusion? by Vellmont · 2003-03-24 21:09 · Score: 1

I don't really know anything about number theory, but I I get a little suspicious when anyone announces a discovery in a field unrelated to their area of expertise. Utah chemists did this in 89 or 90 with Cold Fusion, and it was quickly shown to be bad science by physicists.

Can anyone out their study number theory give us a heads up if they may be on to something, or this is simply just crazy?

--
AccountKiller
1. Re:Physicists pulling a cold fusion? by exp(pi*sqrt(163)) · 2003-03-25 04:26 · Score: 1
  
  This isn't some obscure result that requires sensitive equipment and millions of dollars worth of lab equipment. It's a simple proposition about numbers. Read the article. Do it yourself. It's not hard.
  
  --
  Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
2. Re:Physicists pulling a cold fusion? by l2718 · 2003-03-25 05:54 · Score: 3, Informative
  
  As a number theory graduate student, this looks suspicious. This isn't as bad as last summer, when some string theorists claimed a junk
  proof of the Riemann Hypothesis, but it's close.
  
  Prime numbers are very hard to tackle. Part of the difficulty in this style of problem, as another post points out, is that they are defined multiplicatively, and yet we here care about additive properties (differences in this case).
  
  I have a few concerns with this paper:
  
  1. They look at a really small number of primes (only 10^7 of them). Many false conjectures have been made that way. The most famous case is with the prime number theorem: it's known that up to x there are about x/log(x) primes, and as x grows this estimate becomes more and more accurate. If you do some tests you'll quickly see that there are more than x/log(x) primes up to x for all x you can test for. This was conjectured to be true for all x, until someone proved that actually the difference (# primes up to x) - x/log(x) changes sign infinitely often. The first change is known to happen before x=10^370 -- but try testing that.
  
  2. They use the ansatz Alog(log(x))+B to fit some function of x (the entropy). But for x in the range of concern (at most 10^8), log(log(x)) is essentially constant. Try graphing that function and you'll see for yourself. For all practical purposes (i.e. unless you can run your computer up to numbers like 10^100), doing curve fitting with this function is very suspicious.
  
  My take,
  Lior
3. Re:Physicists pulling a cold fusion? by l2718 · 2003-03-25 06:05 · Score: 1
  
  Another point:
  
  One page 14 (figure 5) they discover the following fact: the difference between the i'th and (i+1)st primes is about log(i).
  
  That is exactly the prime number theorem I mentioned above, conjectured by Gauss around 1800 and proved in 1896 by Hadamard and de la Valee Pussin.
  
  Writing a paper on the distribution of primes and not referring to that is like writing a paper mentioning a discovery that planets move in elliptical orbits, while being ignorant of Kepler's laws or Newton's explanation of them.
  
  Lior
4. Re:Physicists pulling a cold fusion? by Anonymous Coward · 2003-03-25 06:23 · Score: 0
  
  Another point:
  They're physicists trying to do mathematics.
  There is overwhelmimg evidence to suggest that this is a crock before even reading the article. Despite my better judgement I read it anyways. It is a crock. However, it is good exercise for graduate students to find the flaws in the article. For extra credit you can go and wade through the xxx archives and pick all of that crap apart.
EASY ON THE CAPITALS, POINDEXTER by Anonymous Coward · 2003-03-24 21:15 · Score: 0

ujh lkj h hp u ho iuho iuh oiu hoiu ho iuh o uih oiuh oiu ho uh ou ho iuh oui ho uh ou ho uh
Here's the rub by Anonymous Coward · 2003-03-24 21:20 · Score: 5, Interesting

Here's the problem with finding patterns in Primes: It has to do with the way most things in number theory are formulated. Prime numbers are figured out by a process of non-definition and NOT by some form of additive process. An example or two might make that statement a bit clearer:

If I needed, for example, to find a rule that returns only even numbers, my problem is simplicity itself, I have no need to test a given number to determine whether or not it is even, I can force it to be even by applying any number of simple (or complex) formulas that work within the system.

If someone gives me number X, I have no need to know what X is, all I have to do is multiply X by 2 and (after a little inductive reasoning), I have guaranteed that I now have an even number.

Prime numbers are NOT found that way. An even number is determined to have the property 'evenness' from within the number system itself, namely multiplication by 2. It is a simple additive process to include other even numbers into a given set. A prime number on the other hand, forgive the inexactness, can be considered to have the inherent property 'whatever property that created me that is unique to me'.

IOW, each prime number is unalterably unique and furthermore it is unique in a way which is unique to EACH AND EVERY prime number, all by itself. No other prime number has the same property that makes any other prime number unique.

EXAMPLES (bad, I know, but the best I could do at 0430):
the number 7 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 7 and 1, a property that it shares with no other numbers.

the number 17 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 17 and 1, a property that it shares with no other numbers.

the number 21 (not a prime) has the property (among other properties, like 'oddness') that it has the divisors (7 and 3) AND (21 and 1). Only primes get to leave out that AND part.

The prime numbers are the GAPS within the number-system (and in a rather pathological side note - they are also the glue that holds the system together). The definition of a prime number is, put simplistically: ANY number X that is NOT composite.

Saying you have found a pattern in the prime numbers is tantamount to saying that you have a rule that can create prime numbers W/O checking to see if it's true or not. Put another way, it is exactly the same as saying:

"I have a formula P(x) that can always churn out primes, give me a number, any number and after the application of my formula, I can guarantee that it will be a prime number."

If you could do that, I have a whole bunch of NP complete problems for you to work on (and a bone to pick with a certain Mr. Godel).

Any pattern w/in the set of prime numbers would be a formula with an infinite number of rules (an individual rule for each individual prime number, AT LEAST), and anything with an infinite number of rules can be considered completely, totally and irrevocably RANDOM.

Some late night ramblings from a guy who's too tired and lazy to log on.
1. Re:Here's the rub by Anonymous Coward · 2003-03-24 21:37 · Score: 3, Informative
  
  They don't claim that they have a rule that can create prime numbers, they just claim that prime numbers might not be completely random.
  
  Just like if you have a large prime p, p+210 is 4.375 times more likely to be a prime than a random integer around p. Not a rule, but a hint that primes aren't so random.
2. Re:Here's the rub by Scarblac · 2003-03-24 21:42 · Score: 1
  
  the number 7 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 7 and 1, a property that it shares with no other numbers.
  
  the number 17 (a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 17 and 1, a property that it shares with no other numbers.
  
  The number 15 (not a prime) has the unique property (among other properties, like 'oddness') that it has the unique divisors 3 and 5, a property that it shares with no other numbers.
  
  It's also the only number that is equal to 15.
  
  Every number has a special property - in particular, the lowest number that doesn't has the special property "is the lowest number that has no special properties" :-)
  
  --
  I believe posters are recognized by their sig. So I made one.
3. Re:Here's the rub by coyote-san · 2003-03-25 04:53 · Score: 1
  
  "I have a formula P(x) that can always churn out primes, give me a number, any number and after the application of my formula, I can guarantee that it will be a prime number."
  
  That's trivial. P(x+1)=1+PI{P(i) for i = 0 to x}, P(0) = 1 or 2, depending on whether you want to list 1 as a prime number. That's been know since antiquity.
  What would blow open mathematics would be a non-trivial function to determine all prime numbers, in order, with at most a finite number of known omissions.
  
  --
  For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
4. Re:Here's the rub by SomeGuyFromCA · 2003-03-25 06:16 · Score: 1
  
  > "I have a formula P(x) that can always churn out primes, give me a number, any number and after the application of my formula, I can guarantee that it will be a prime number."
  
  A non trivial formula, you mean. Otherwise the following applies:
  
  P(x) = 7(x/x)
  
  --
  if the answer isn't violence, neither is your silence / freedom of expression doesn't make it alright
5. Re:Here's the rub by Anonymous Coward · 2003-03-25 06:19 · Score: 0
  
  For fun I tried your formula with all the primes between 1000 and 1100. Tabulated are p, p+210, and isprime(p+210):
  
  1009, 1219, false
  1013, 1223, true
  1019, 1229, true
  1021, 1231, true
  1031, 1241, false
  1033, 1243, false
  1039, 1249, true
  1049, 1259, true
  1051, 1261, false
  1061, 1271, false
  1063, 1273, false
  1069, 1279, true
  1087, 1297, true
  1091, 1301, true
  1093, 1303, true
  1097, 1307, true
  
  10 of the "p+210 numbers" are prime (out of 16). Amazing.
6. Re:Here's the rub by Anonymous Coward · 2003-03-25 06:33 · Score: 0
  That's trivial. P(x+1)=1+PI{P(i) for i = 0 to x}, P(0) = 1 or 2, depending on whether you want to list 1 as a prime number. That's been know since antiquity.
  
  Let's see....
  
  P(0) = 1
  
  P(1) = 1+(1) = 2
  
  P(2) = 1+(1*2) = 3
  
  P(3) = 1+(1*2*3) = 7
  
  P(4) = 1+(1*2*3*7) = 43
  
  P(5) = 1+(1*2*3*7*43) = 1807 = 13*139
  
  This expression is part of a proof that there are an infinite number of primes: if the set of primes were finite, then their product plus 1 would be a new prime not divisible by any in the set; thus the set cannot be finite. If you try this with a set that does not include all the primes, as in P(5) above, there is no guarantee that the result will be a prime.
7. Re:Here's the rub by stu-pendous · 2003-03-25 07:33 · Score: 1
  
  Dude,
  That formula is so wrong...
  for P(0) = 2 Then
  P(1) = 3 o.k.
  P(2) = 7 o.k.
  P(3) = 43 o.k.
  P(4) = 1807 (whoa! 13 * 139)
  
  Perhaps you meant something else?
8. Re:Here's the rub by Anonymous Coward · 2003-03-25 09:54 · Score: 0
  
  If you could do that, I have a whole bunch of NP complete problems for you to work on (and a bone to pick with a certain Mr. Godel).
  
  It's been done. It's a complicated formula, so pull out your TeX:
  
  p(n)=1+\sum_{m=1}^{2^n}\lfloor n^{1/n} (\sum_{k=1}^m\lfloor\cos^2 \pi
  {(k-1)!+1\over k}\rfloor)^{-1/n}\rfloor
  
  The function p(n) is prime for every value of n, and there's only a finite set of operations to do!
  
  It's perfectly valid, and sadly, utterly useless. The key feature is Wilson's Theorem (p is prime iff (p-1)! = -1 mod p). The (k-1)!+1 in the cosine picks up on that, and the rest makes everything come out as a nice integer.
9. Re:Here's the rub by n1vux · 2003-03-25 12:28 · Score: 1
  
  Hardly amazing, although it would be if not predicted by number theory. Note that you shouldn't decide 10 of 16 is amazing until you check how many of the range would be prime normally, 15 of 1000. This seems to support the ratio given, but doesn't equal it. By the way, the phenomenon holds up on the first thousand primes quite nicely, but still not exactly 4.375.
  For a hint at why it's so, Google +4.375 Primes 210 to get
  Sieve of Eratosthenes ... list of smallest primes can be extended, eg including 5 and 7, and we need only to consider 48 numbers out of 210, achieving a speed-up factor of even 4.375. ... wwwhomes.uni-bielefeld.de/achim/prime_sieve.html - 12k
  
  And also examine report of 7 Consecutive Primes in Arithmetic sequence at 7 consec primes in AP(1995, NMBRTHRY list archive).
  I would be interested in a reference to the actual number-theory statement proof of what the ratio in the asymptotic limit actually is.
  -- Bill N1VUX IANA-Mathematician, but I played one in college. I had a .sig when USEnet was the signet.
10. Re:Here's the rub by Anonymous Coward · 2003-03-25 17:41 · Score: 0
  
  I would be interested in a reference to the actual number-theory statement proof of what the ratio in the asymptotic limit actually is.
  
  Let r = product(p/(p-1), p is prime)
  
  log(r) = sum(log(p/(p-1)), p is prime)
  >= sum(1/p, p is prime)
  
  That last sum is known to be divergent. Therefore the asymptotic ratio r is infinity.
11. Re:Here's the rub by Amousha · 2003-03-29 17:55 · Score: 1
  
  Not quite true.
  
  You're posits are true, just not the consequence.
  
  What you might end up doing, upon examining the statistical distribution of primes (and upon detecting a pattern), is come up with a new branch of mathematics (a number system) in which the formula for prime numbers might even be a constant (a property of the space).
  
  omard-out
12. Re:Here's the rub by freaq · 2003-03-29 18:24 · Score: 1
  
  No, no, no. It's not a matter of if you want to or not. If you do, there's a world of mathematicians who will tell you that what you are doing might not qualify as mathematics.
  
  One is not prime. Prime means having exactly two divisors, one of which is one. Please find enclosed a snider definition and commentary.
  
  (Yes, I took MATH 230, but no, I didn't pass. Sorry I couldn't hold on, Clive.)
  
  --
  united states nuclear device terrorist bioweapon encryption cocaine korea syria iran iraq columbia cuba
The pattern ... by Tux2000 · 2003-03-24 22:20 · Score: 1

"3 is prime, 5 is prime, 7 is prime, 9 is, um, experimental error, 11 is prime, 13 is prime--looks good."

--
Denken hilft.
Re:sad news by Anonymous Coward · 2003-03-24 22:32 · Score: 0

Very nice theme, sir, but you could brush it up a little, give a couple of examples his 'contributions' to world culture, etc.
I found a pattern! by Dahan · 2003-03-24 23:15 · Score: 1

Hey, I think I found a pattern to the prime numbers!!!1!! While I admit I haven't had a chance to try them all, it looks like primes greater than 3 are of the form 6n-1 or 6n+1, where n is an integer.
5=6*1-1, 7=6*1+1, 11=6*2-1, 13=6*2+1, 17=6*3-1, 19=6*3+1, ..., 3141592799=6*523598800-1, 3141592801=6*523598800+1, ...
Pretty cool, huh? So where's my Field's Medal? Or at least I should get published in Nature for this!
1. Re:I found a pattern! by KDan · 2003-03-25 00:07 · Score: 1
  
  3141592799 / 3 = 1047197600
  
  So not a prime.
  
  Daniel
  
  --
  Carpe Diem
2. Re:I found a pattern! by Dahan · 2003-03-25 00:48 · Score: 1
  
  You might try setting your calculator so that it doesn't round to integer. 3141592799 is prime. 31415927299 / 3 = 1047197599 + 2/3.
  P.S. Another thing worthy of a Nature article... an integer is evenly divisible by 3 if the sum of its digits is evenly divisible by 3. 3+1+4+1+5+9+2+7+9+9=50. 5+0=5. 5 is not evenly divisible by 3. Therefore neither is 31415927299.
  P.P.S. 1047197600 has two zeros at the end. If you multiply it by any integer, the product will have at least two zeros at the end. Therefore a trivial inspection would show that 3*1047197600 != 3141592799.
3. Re:I found a pattern! by Dahan · 2003-03-25 00:56 · Score: 1
  
  Bah, s/31415927299/3141592799/g...
4. Re:I found a pattern! by itsme1234 · 2003-03-25 01:07 · Score: 5, Insightful
  
  Of course they are prime ! ANY number is either:
  
  6n (not prime of course)
  6n+1
  6n+2 (not prime of course)
  6n+3 (not prime of course)
  6n+4 (not prime of course)
  6n+5
  
  And 6n+5 is the same as 6(n+1)-1 so indeed you are right. You deserve a price for finding a 6th grade theorem.
5. Re:I found a pattern! by forsetti · 2003-03-25 02:12 · Score: 1
  
  ALL primes will have to be of the form:
  2n+1 (not divisible by 2)
  3n+1, 3n+2 (not divisible by 3)
  5n+1, 5n+2, 5n+3, 5n+4 (not divisible by 5)
  etc for all Pn+d , where P is prime, n is an integer, and d is an integer 1<=d<P
  
  So, your theorem is correct, as all primes will have to fit the form ((2n+1) AND ((3n+1) OR (3n+2))), which can be written as ((6n+1) OR (6n-1)), but unfortunately, this does not help much.
  
  It would be much more helpful to find an equation stating that all numbers of the single form (...) are prime, instead of all primes fit the form (...).
  
  --
  10b||~10b -- aah, what a question!
6. Re:I found a pattern! by eingram · 2003-03-25 04:39 · Score: 1
  
  Ding! Correct!
  6(9) - 1 = 53
  6(56) + 1 = 337
  
  Bzzt. Incorrect!
  6(9) + 1 = 55
  6(56) - 1 = 335
  
  What you need is a GUT (grand unified theory). It's like trying to combine quantum mechanics with general relativity. Good luck. :)
7. Re:I found a pattern! by jat2 · 2003-03-25 05:55 · Score: 1
  
  Of course they are prime ! ANY number is either:
  6n (not prime of course)
  6n+1
  6n+2 (not prime of course)
  6n+3 (not prime of course)
  6n+4 (not prime of course)
  6n+5
  Do you mean for all integers n = 1, 2, 3, ... or do you start at zero? Either way, what about the number 3? If you start at n=0, then 6n+3 = 3, but you claim that 6n+3 is "not prime of course," so your claims need to be checked more carefully.
  However, I agree with the overall point of your post.
8. Re:I found a pattern! by Anonymous Coward · 2003-03-25 06:35 · Score: 0
  
  The statement wasn't "all numbers of the form 6n(+/-)1 are prime", it was "all primes [greater than 6] are of the form 6n[+/-]1". And as other posters have mentioned this is both true and trivially obvious. It is in fact a single 'hole' in the sieve of Erastothenes.
9. Re:I found a pattern! by Noren · 2003-03-25 07:13 · Score: 1
  
  That doesn't work for 5^2 (6*4+1=25). Let's extend that by saying primes greater than 5 are in the form 30n-13, 30n-11, 30n-7, 30n-1, 30n+1, 30n+7, 30n+11, or 30n+13, where n is an integer. Surely we've now got a working method!
  But that doesn't work for 7^2 (2*30-11), so we'll modify that to : Primes greater than 7 are in the form 210(=2*3*5*7) plus or minus one or (any of the prime numbers less than 105 and greater than 7).
  But that doesn't work for 11^2(210-89), so...
  Repeat this process for all the prime numbers and you'll have a formula you can use to to determine all the prime numbers!
10. Re:I found a pattern! by Anonymous Coward · 2003-03-25 08:51 · Score: 0
  
  Yeah, you're right.
  
  But, um, seriously. Anybody can miss something obvious (no matter how skilled they are).
  
  That 6th grade remark was extremely childish.
11. Re:I found a pattern! by Dahan · 2003-03-25 10:00 · Score: 1
  
  You deserve a price for finding a 6th grade theorem.
  Yes! Fields Medal! Now!! Before I get too old for it...
12. Re:I found a pattern! by kazad · 2003-03-25 16:14 · Score: 1
  
  I think you pointed out something interesting, others were being unnecessarily harsh. Basically, your statement is: Any prime number must be of the form 6n + 1 or 6n - 1. The inverse is not necessarily true: 6n + 1 doesn't necessarily go to primes. Likewise, all primes are odd, but not all odds are prime.
13. Re:I found a pattern! by Muhammar · 2003-03-25 16:49 · Score: 1
  
  n=5: 6n+5=35 (not prime enuf)
  
  --
  I doubt that we will ever figure out - and I suspect that even if we did figure out we couldn't do much about it
14. Re:I found a pattern! by Anonymous Coward · 2003-03-30 11:12 · Score: 0
  
  The property you define is that of a number relatively prime to 6. Since all prime numbers (except 2 and 3, which you exclude) will be by definition relatively prime to 6, you have a nice tautology.
They mostly share a quality by obtuse · 2003-03-24 23:31 · Score: 1

Not multiples of (pick a number other than 1 & the prime.) They're defined by the patterns they don't fit. That looks like an irregular or near fit to a pattern.

I said all primes are odd in an earlier post. Sorry, all primes but the number two are odd.

I hacked up a perl script to demonstrate what these guys were describing. I don't want to drop it in here, because it's a shameful late night hack, but it's in my journal. It generates primes, increments, intervals, and a running total of the intervals, since Kumar says they tend to follow each other in opposition closely. I'm still unconvinced they're onto anything novel, but I'll look again in the AM.

--
Assembly is the reverse of disassembly.
1. Re:They mostly share a quality by zeugma-amp · 2003-03-25 04:57 · Score: 1
  
  results of your script:
  ./primer.pl Number found where operator expected at ./primer.pl line 7, near "] 1" (Missing operator before 1?) Number found where operator expected at ./primer.pl line 28, near ") 8193" (Missing operator before 8193?) syntax error at ./primer.pl line 7, near "] 1" syntax error at ./primer.pl line 28, near ") 8193" Execution of ./primer.pl aborted due to compilation errors.
  Sorry :-)
  
  --
  This is an ex-parrot!
I've got one! by Andy_R · 2003-03-25 01:00 · Score: 2, Funny

"I have a formula P(x) that can always churn out primes, give me a number, any number and after the application of my formula, I can guarantee that it will be a prime number."

If you could do that, I have a whole bunch of NP complete problems for you to work on (and a bone to pick with a certain Mr. Godel).

x-x+7 gives a prime number for every value of x ;-)

--
A pizza of radius z and thickness a has a volume of pi z z a
1. Re:I've got one! by kilonad · 2003-03-25 02:12 · Score: 1
  
  He said x-x+7 is prime. Not x+x+7. X-X+7 always equals 7, and is therefore always prime.
2. Re:I've got one! by babbage · 2003-03-25 04:57 · Score: 1
  
  The funny thing is that this formula actually plays into Godel's theorem, not against it. Yay incompleteness :)
  
  --
  DO NOT LEAVE IT IS NOT REAL
Anyone can test this theory out. by pauldy · 2003-03-25 02:08 · Score: 2, Interesting

Take the first 1000 primes from the site listed. Put them in your favorite spreadsheet. Then use the formula they give to find out they are mostly full of it. For they first few it looks like a pattern is forming then it looks like nothing but noise when plotted. I can't believe no one even tryed this before they actually published this article.
1. Re:Anyone can test this theory out. by michaelggreer · 2003-03-25 08:10 · Score: 2, Informative
  
  - I can't believe no one even tryed this before they actually published this article.
  
  Well, they did. Thats what all the above gags are about, that these physicists are unaware of prior, basic "Fun with Primes!" work. Nature too, evidently.
2. Re:Anyone can test this theory out. by rueba · 2003-03-30 07:17 · Score: 1
  
  Was this specific result already found?
  
  I only read the abstract, but it seems they were only looking at the 'increments' between the gaps in prime numbers.
  
  The gaps between prime numbers have been well studied, but perhaps no one has bothered to look at the increments.
  
  Still, I agree that this is does not look all that surprising since the distribution of primes is well-studied, but they may have looked at some wrinkle that people had not looked at before.
  
  Also, the Nature write-up was particularly clueless. "No one has yet proved that their[primes] occurrence follows any pattern, or whether there is definitely no pattern."
  
  Please!
  
  --
  The only reason all cover-ups appear to fail is that you never hear about the ones that succeed.
vapid... by JiffyPop · 2003-03-25 02:27 · Score: 1

wow, another random non-mathematician finding isolated patterns in a mathematically complex sequence of numbers...

the patterns they describe are likely nothing more than side effects that can be produced using a number sieve. that seems to be what most of the "prime formulas" that people come up with can be reduced to.
Parallels with Carl Sagan's "Contact" by Anonymous Coward · 2003-03-25 03:06 · Score: 1, Interesting

This sounds spookily like the ending in Contact (only in the book, not the film) where researchers find a message buried in the seemingly random digits of Pi. The implication was that the builders of the universe had left behind their signature.

Perhaps these guys should map out their sequences of prime number differences to see if it generates a picture ?
Yes there is pattern.. by Anonymous Coward · 2003-03-25 03:20 · Score: 0

none of these numbers are divisible without a reminder except for 1 and themselves!?
Skip right to the paper. by molo · 2003-03-25 04:00 · Score: 2, Informative

Want the details? Ignore the watered-down article and skip right to the research paper.. all greek to me, but has some interesting plots:

Information Entropy and Correlations in Prime Numbers -- Abstract

Information Entropy and Correlations in Prime Numbers [PDF]

Information Entropy and Correlations in Prime Numbers [Postscript]

-molo

--
Using your sig line to advertise for friends is lame.
1. Re:Skip right to the paper. by Engelbot · 2003-03-28 17:06 · Score: 1
  
  All I see whenever I load the PDF or Postscript files is the abstract. Does anybody know where the full paper is?
2. Re:Skip right to the paper. by molo · 2003-03-29 14:50 · Score: 1
  
  Looks like they yanked it and put the abstract in its place. I don't have a copy saved, sorry.
  
  -molo
  
  --
  Using your sig line to advertise for friends is lame.
Some numbers to look at by big_alpaca · 2003-03-25 04:20 · Score: 2, Interesting

So here is 5 minutes of mathemetica output to look at. dlist is the list of differences between sequential primes. ilist is the increment between subsequent differences. Have fun.

ilist = dlist = {}; Do[dlist = Append[dlist, Prime[n + 1] - Prime[n]], {n, 1000}]; Do[ilist = Append[ilist, dlist[[n + 1]] - dlist[[n]]], {n, 999} ]; dlist {1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6, 4, 6, 8, 4, 2, 4, 12, 8, 4, 8, 4, 6, 12, 2, 18, 6, 10, 6, 6, 2, 6, 10, 6, 6, 2, 6, 6, 4, 2, 12, 10, 2, 4, 6, 6, 2, 12, 4, 6, 8, 10, 8, 10, 8, 6, 6, 4, 8, 6, 4, 8, 4, 14, 10, 12, 2, 10, 2, 4, 2, 10, 14, 4, 2, 4, 14, 4, 2, 4, 20, 4, 8, 10, 8, 4, 6, 6, 14, 4, 6, 6, 8, 6, 12, 4, 6, 2, 10, 2, 6, 10, 2, 10, 2, 6, 18, 4, 2, 4, 6, 6, 8, 6, 6, 22, 2, 10, 8, 10, 6, 6, 8, 12, 4, 6, 6, 2, 6, 12, 10, 18, 2, 4, 6, 2, 6, 4, 2, 4, 12, 2, 6, 34, 6, 6, 8, 18, 10, 14, 4, 2, 4, 6, 8, 4, 2, 6, 12, 10, 2, 4, 2, 4, 6, 12, 12, 8, 12, 6, 4, 6, 8, 4, 8, 4, 14, 4, 6, 2, 4, 6, 2, 6, 10, 20, 6, 4, 2, 24, 4, 2, 10, 12, 2, 10, 8, 6, 6, 6, 18, 6, 4, 2, 12, 10, 12, 8, 16, 14, 6, 4, 2, 4, 2, 10, 12, 6, 6, 18, 2, 16, 2, 22, 6, 8, 6, 4, 2, 4, 8, 6, 10, 2, 10, 14, 10, 6, 12, 2, 4, 2, 10, 12, 2, 16, 2, 6, 4, 2, 10, 8, 18, 24, 4, 6, 8, 16, 2, 4, 8, 16, 2, 4, 8, 6, 6, 4, 12, 2, 22, 6, 2, 6, 4, 6, 14, 6, 4, 2, 6, 4, 6, 12, 6, 6, 14, 4, 6, 12, 8, 6, 4, 26, 18, 10, 8, 4, 6, 2, 6, 22, 12, 2, 16, 8, 4, 12, 14, 10, 2, 4, 8, 6, 6, 4, 2, 4, 6, 8, 4, 2, 6, 10, 2, 10, 8, 4, 14, 10, 12, 2, 6, 4, 2, 16, 14, 4, 6, 8, 6, 4, 18, 8, 10, 6, 6, 8, 10, 12, 14, 4, 6, 6, 2, 28, 2, 10, 8, 4, 14, 4, 8, 12, 6, 12, 4, 6, 20, 10, 2, 16, 26, 4, 2, 12, 6, 4, 12, 6, 8, 4, 8, 22, 2, 4, 2, 12, 28, 2, 6, 6, 6, 4, 6, 2, 12, 4, 12, 2, 10, 2, 16, 2, 16, 6, 20, 16, 8, 4, 2, 4, 2, 22, 8, 12, 6, 10, 2, 4, 6, 2, 6, 10, 2, 12, 10, 2, 10, 14, 6, 4, 6, 8, 6, 6, 16, 12, 2, 4, 14, 6, 4, 8, 10, 8, 6, 6, 22, 6, 2, 10, 14, 4, 6, 18, 2, 10, 14, 4, 2, 10, 14, 4, 8, 18, 4, 6, 2, 4, 6, 2, 12, 4, 20, 22, 12, 2, 4, 6, 6, 2, 6, 22, 2, 6, 16, 6, 12, 2, 6, 12, 16, 2, 4, 6, 14, 4, 2, 18, 24, 10, 6, 2, 10, 2, 10, 2, 10, 6, 2, 10, 2, 10, 6, 8, 30, 10, 2, 10, 8, 6, 10, 18, 6, 12, 12, 2, 18, 6, 4, 6, 6, 18, 2, 10, 14, 6, 4, 2, 4, 24, 2, 12, 6, 16, 8, 6, 6, 18, 16, 2, 4, 6, 2, 6, 6, 10, 6, 12, 12, 18, 2, 6, 4, 18, 8, 24, 4, 2, 4, 6, 2, 12, 4, 14, 30, 10, 6, 12, 14, 6, 10, 12, 2, 4, 6, 8, 6, 10, 2, 4, 14, 6, 6, 4, 6, 2, 10, 2, 16, 12, 8, 18, 4, 6, 12, 2, 6, 6, 6, 28, 6, 14, 4, 8, 10, 8, 12, 18, 4, 2, 4, 24, 12, 6, 2, 16, 6, 6, 14, 10, 14, 4, 30, 6, 6, 6, 8, 6, 4, 2, 12, 6, 4, 2, 6, 22, 6, 2, 4, 18, 2, 4, 12, 2, 6, 4, 26, 6, 6, 4, 8, 10, 32, 16, 2, 6, 4, 2, 4, 2, 10, 14, 6, 4, 8, 10, 6, 20, 4, 2, 6, 30, 4, 8, 10, 6, 6, 8, 6, 12, 4, 6, 2, 6, 4, 6, 2, 10, 2, 16, 6, 20, 4, 12, 14, 28, 6, 20, 4, 18, 8, 6, 4, 6, 14, 6, 6, 10, 2, 10, 12, 8, 10, 2, 10, 8, 12, 10, 24, 2, 4, 8, 6, 4, 8, 18, 10, 6, 6, 2, 6, 10, 12, 2, 10, 6, 6, 6, 8, 6, 10, 6, 2, 6, 6, 6, 10, 8, 24, 6, 22, 2, 18, 4, 8, 10, 30, 8, 18, 4, 2, 10, 6, 2, 6, 4, 18, 8, 12, 18, 16, 6, 2, 12, 6, 10, 2, 10, 2, 6, 10, 14, 4, 24, 2, 16, 2, 10, 2, 10, 20, 4, 2, 4, 8, 16, 6, 6, 2, 12, 16, 8, 4, 6, 30, 2, 10, 2, 6, 4, 6, 6, 8, 6, 4, 12, 6, 8, 12, 4, 14, 12, 10, 24, 6, 12, 6, 2, 22, 8, 18, 10, 6, 14, 4, 2, 6, 10, 8, 6, 4, 6, 30, 14, 10, 2, 12, 10, 2, 16, 2, 18, 24, 18, 6, 16, 18, 6, 2, 18, 4, 6, 2, 10, 8, 10, 6, 6, 8, 4, 6, 2, 10, 2, 12, 4, 6, 6, 2, 12, 4, 14, 18, 4, 6, 20, 4, 8, 6, 4, 8, 4, 14, 6, 4, 14, 12, 4, 2, 30, 4, 24, 6, 6, 12, 12, 14, 6, 4, 2, 4, 18, 6, 12, 8} ilist {1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2, -2, 2, 2, 0, -4, 4, -2, -2, 4, -2, 2, 2, -4, -2, 2, -2, 2, 10, -10, 2, -4, 8, -8, 4, 0, -2, 2, 0, -4, 8, -8, 2, -2, 10, 0, -8, -2, 2, 2, -4, 8, -4, 0, 0, -4, 4, -2, -2, 8, 4, -10, -2, 2, 10, -8, 4, -8, 2, 2, 2, -2, 0, -2, 2, 2, -4, 4, 2, -8, 8, -8, 4, -2, 2, 2, -4, -2, 2, 8, -4, -4, 4, -4, 2, 6, -10, 16, -12, 4, -4, 0, -4, 4, 4, -4, 0
Unexpected Patterns of Diagonal Lines by chemstar · 2003-03-25 04:33 · Score: 2, Informative

Don't forget the Prime Spiral.

This construction was first made by Polish-American mathematician Stanislaw Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific meeting. While drawing a grid of lines, he decided to number the intersections according to a spiral pattern, and then began circling the numbers in the spiral that were primes. Surprisingly, the circled primes appeared to fall along a number of diagonal straight lines or, in Ulam's slightly more formal prose, it "appears to exhibit a strongly nonrandom appearance"

More info.
1. Re:Unexpected Patterns of Diagonal Lines by Anonymous Coward · 2003-03-30 07:53 · Score: 0
  
  Of course there is a diagonal pattern. All prime numbers are of the form 2n+1, so any two squares next to each other can't both be primes.
Parallels with Lem's "His Master's Voice" by metamatic · 2003-03-25 04:57 · Score: 1

See also "His Master's Voice" by Stanislaw Lem, which I think is far more mindblowing.

--
GCHQ Quantum Insert installed. If only our tongues were made of glass, how much more careful we would be when we speak
11:15, restate my assumptions by anthony_dipierro · 2003-03-25 05:06 · Score: 1

Hold on. You have to slow down. You're losing it. You have to take a breath. Listen to yourself. You're connecting a computer bug I had with a computer bug you might have had and some religious hogwash. You want to find the number 216 in the world, you will be able to find it everywhere. 216 steps from a mere street corner to your front door. 216 seconds you spend riding on the elevator. When your mind becomes obsessed with anything, you will filter everything else out and find that thing everywhere.

2*2*2*3*3*3=216

12:50, press Return.
Of course primes are nonrandom... by Effugas · 2003-03-25 06:46 · Score: 1

They're intimately tied to their position along the integer continuum. It's just that the complexity of determining primality (the information content, in fact) increases with the position.

Randomness is not actually entropy.

--Dan
1. Re:Of course primes are nonrandom... by n1vux · 2003-03-26 05:12 · Score: 2, Informative
  
  Right, Primes have intrinsic information content, so we shouldn't be surprised someone could measure their entropy if they tried. These physicists used their own data-analytic tools to measure this in an empirical way. Whether this provides a new insight to the number theorists or not is yet to be seen, but applying new tools to problems with which mathematicians have been "stuck" has sometimes provided a needed boost.
  The pattern they've found is a logarithmic distribution, it seems, according to their abstract. (I need to make time to read the full paper.) This is not unexpected, the Newcombe distribution known as Benford's Law (1) is a well-known logarithmic distribution applicable to most naturally occurring numbers. Benford's law is
  F(d)=log(1+1/d)
  which applies of course only to the non-zero data in the dataset; it generalizes to
  F(ddd..d)=log(1+1/ddd..d)
  
  While their reported entropy power law is logarithmic, Benford's law doesn't appear to fit the prime interval increments. This leaves open the power law the physicists have found is different, suggesting the possibility that there is something interesting and new in their finding. We can hope this gives the number theorists some fresh insight. Since it was posted to the Physics :: Condensed Matter directory of arXiv, it may be a while before the real number theorists even notice it; sci.math.research quite reasonably gets postings of the new listings of only the Math subdirs weekly. We can hope Baez cross-posts it.
  --Bill
  IANA-Mathematician, but I almost was one and still pretend
They're all over the place ... by Ashtead · 2003-03-25 07:16 · Score: 1

Now, saying "all primes but 2 are odd", is just the same as saying "all primes except 2 do not divide evenly by 2".
FWIW, I can offer the following additional observation: All primes except 2 and 5 must end with 1, 3, 7 or 9, and these must be matching one of:
30n+7 30n+11 30n+13 30n+17 30n+19 30n+23 30n+29 30n+31
for all n>=0
I guess similar arguments may be made for including further factors 7 (210n+7 etc) and 11 (2310n+7 and so on) but I suspect this gets too unwieldy too soon to be very useful.
Finally, I wonder where they found that "speed limit 31 mph" sign. I have seen speed limits of 13 and 19 mph elsewhere, so this could even be a bit fascinating. Also, I wonder how much of a coincidence it is that the numbers 3, 31, 17, and 13, can be found in the URL of the article.

--
SIGBUS @ NO-07.308
1. Re:They're all over the place ... by jamesh · 2003-03-30 17:13 · Score: 1
  
  'odd' is just a property of any number not divisable evenly by 2, so as you say, "all primes except 2 are not divisable evenly by 2."
  
  to extend that...
  
  all primes except 3 are not divisable by 3.
  all primes except 5 are not divisable by 5.
  all primes except 7 are not divisable by 7. ...
  all primes except x are not divisable by x.
  (where x is prime).
  
  that is by definition though, it's not a proof.
  
  odd, (and for that matter, evenly divisable by 5 or 10) is only visible in our normal number system because it is base 10 and 10 is evenly divisable by 2, 5 and 10, so we can tell at a glance for a number printed in base 10.
  
  if we used a base 3 number system, or some base divisable by 3, all numbers divisable by 3 would be instantly recognisable too.
How to prove that all odd numbers are prime by dargaud · 2003-03-25 08:02 · Score: 4, Funny

"It was mentioned on CNN that the new prime number discovered recently is four times bigger than the previous record." John Blasik

"You know what seems odd to me? Numbers that aren't divisible by two." Michael Wolf.

"I don't get even, I get odder."
Well, the problem "How to prove that all odd numbers are prime" has different solutions whether you are a:
Mathematician: 1 is prime, 3 is prime, 5 is prime, 7 is prime, and by induction we have that all the odd integers are prime.
Physicist: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is an experimental error...
Engineer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime...
Chemist: 1 prime, 3 prime, 5 prime... hey, let's publish!
Modern physicist using renormalization: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... 9/3 is prime, 11 is prime, 13 is prime, 15 is ... 15/3 is prime, 17 is prime, 19 is prime, 21 is ... 21/3 is prime...
Quantum Physicist: All numbers are equally prime and non-prime until observed.
Professor: 1 is prime, 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
Confused Undergraduate: Let p be any prime number larger than 2. Then p is not divisible by 2, so p is odd. QED
Measure nontheorist: There are exactly as many odd numbers as primes (Euclid, Cantor), and exactly one even prime (namely 2), so there must be exactly one odd nonprime (namely 1).
Cosmologist: 1 is prime, yes it is true....
Computer Scientist: 1 is prime, 10 is prime, 11 is prime, 101 is prime...
Programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 will be fixed in the next release, ...
C programmer: 01 is prime, 03 is prime, 05 is prime, 07 is prime, 09 is really 011 which everyone knows is prime, ...
BASIC programmer: What's a prime?
COBOL programmer: What's an odd number?
Windows programmer: 1 is prime. Wait...
Mac programmer: Now why would anyone want to know about that? That's not user friendly. You don't worry about it, we'll take care of it for you.
Bill Gates: 1. No one will ever need any more than 1.
ZX-81 Computer Programmer: 1 is prime, 3 is prime, Out of Memory.
Pentium owner: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 8.9999978 is prime...
GNU programmer: % prime
usage: prime [-nV] [--quiet] [--silent] [--version] [-e script] --catenate --concatenate | c --create | d --diff --compare | r --append | t --list | u --update | x -extract --get [ --atime-preserve ] [ -b, --block-size N ] [ -B, --read-full-blocks ] [ -C, --directory DIR ] [--checkpoint ] [ -f, --file [HOSTNAME:]F ] [ --force-local ] [ -F, --info-script F --new-volume-script F ] [-G, --incremental ] [ -g, --listed-incremental F ] [ -h, --dereference ] [ -i, --ignore-zeros ] [ --ignore-failed-read ] [ -k, --keep-old-files ] [ -K, --starting-file F ] [ -l, --one-file-system ] [ -L, --tape-length N ] [ -m, --modification-time ] [ -M, --multi-volume ] [ -N, --after-date DATE, --newer DATE ] [ -o, --old-archive, --portability ] [ -O, --to-stdout ] [ -p, --same-permissions, --preserve-permissions ] [ -P, --absolute-paths ] [ --preserve ] [ -R, --record-number ] [ [-f script-file] [--expression=script] [--file=script-file] [file...]
prime: you must specify exactly one of the r, c, t, x, or d options
For more information, type "prime --help''
Unix programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, ...
Segmentation fault, Core dumped.
Computer programmer: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is ...

--
Non-Linux Penguins ?
1. Re:How to prove that all odd numbers are prime by plluke · 2003-03-30 07:38 · Score: 1
  
  1 is a prime? Last I checked one is not a prime...
  
  --
  "The Cube": it just wouldn't be the same without fellatio "Corey Kosak": It just wouldn't be the same... oh, looks like
2. Re:How to prove that all odd numbers are prime by dargaud · 2003-03-30 13:32 · Score: 1
  
  Haa, at least there's one person listening during courses...
  
  --
  Non-Linux Penguins ?
Most common prime in nature? by dalek_killer · 2003-03-25 08:38 · Score: 1

But what is the most commonly found prime number that turns up in nature
the undefined-ness of division by zero by ses4j · 2003-03-25 18:43 · Score: 1

x/0 isn't necessarily infinity (as in +infinity). Think about it this way. Yes, it's true that:

1/1 = 1, 1/.5 = 2, 1/.25 = 4, etc, etc, so by that pattern 1/0 is indeed +infinity.

But, what about:

1/-1 = -1, 1/-.5 = -2, 1/-.25 = -4, etc, etc, so by THIS pattern, 1/0 is -infinity.

So it's undefined. It's kinda both positive infinity and negative infinity at the same time.
1. Re:the undefined-ness of division by zero by JDWTopGuy · 2003-03-26 12:11 · Score: 1
  
  Interesting. All along I thought I just had a dumb-butt idea that somebody was going to shoot down in a half a second.
  
  It's kinda both positive infinity and negative infinity at the same time.
  
  Wouldn't that make it exactly zero because of +/- infinity cancelling out?
  
  Oh well, there goes the kewlness of infinity. :-)
  
  --
  Ron Paul 2012
Re:Immicibility ;p HI commie fuck tsarkon reports by Anonymous Coward · 2003-03-25 20:45 · Score: 0

hi communist puke fuck how are you. you fucking mediocritomaton career loser patentless poor fag.

how is being a poor loser non contributing puke asshole? is it fun?

you puke bitch. you fat sexless loser pigfuck shitstaining cant afford shit pigfucking anus pie.
Looks like the paper has been pulled by MonkeyBoyo · 2003-03-29 05:35 · Score: 1

When you try to get any of the full text versions from http://xxx.lanl.gov/abs/cond-mat/0303110 all you get is the abstract.
1. Re:Looks like the paper has been pulled by Anonymous Coward · 2003-04-01 05:02 · Score: 0
  
  You have to look at v1 of the paper, it is in full length. v2 only has the abstract.
Primes by Anonymous Coward · 2003-03-30 09:34 · Score: 0

What happens if you take prime numbers... and make a prime reflector ? like a parabolic reflector, but a prime number derived one ? How does stuff bounce ? Nah! Too much beer again isn't it :-)
Just in case... (C) me! 2003
Prime numbers by Anonymous Coward · 2003-03-30 09:49 · Score: 0

Have a special significance to religious people

http://numerical19.tripod.com/619.htm
http://fa kir60.tripod.com/importanceof19.htm
http://www.ma laysia.net/lists/sangkancil/1999-01/m sg01546.html
http://www.utm.edu/research/primes/
http://www.geocities.com/aliadams/19.htm
http:// www.submission.org/miracle/proof2.html

6 from the top of my google
I would have done 19 but I got bored :P

Salaam!
Goldston's Result by limitpoint · 2003-03-30 10:01 · Score: 1

Goldston's work is far more profound and interesting than most of the commenters seem to realize, which is to be expected, given the level of ignorance of the average poster. First of all, Goldston (and that Turkish chap) did not ``discover'' any new pattern among the primes -- mathematicans have long conjected that the prime numbers get very close together infinitely often. Indeed, the so called Twin Prime Conjecture asserts that there are infinitely many consecutive primes p,q (p p), such that q - p k*ln(q) ? What is this question getting at? Well, according to the Prime Number Theorem, which was proved in the late 19th century, the number of primes in [2,x] is, asymptotically, x/ln(x). Another way of saying the same thing is that the average gap between consecutive primes in [2,x] is about ln(x). Well, so this begs the question: How often are the gaps between consecutive primes in [2,x] much smaller than this average (that is, ln(x)), and how often are they much larger than the average? This is the source of the ``q-p k*ln(q)'' question above. A whole string of mathematicians worked on this small gaps question for decades, and the best result prior to Goldston's, which was due to H. Maier, was that there are infinitely many consecutive primes p,q such that q - p 0.2 ln(q) (actually, the constant here is a little more than 0.2). Using an ingenious new idea (I have read Goldston's paper) that combines approximation theory, a method called amplification, the Bombieri-Vinogradov theorem, as well as approximate von Mangoldt functions, Goldston has proved this short gaps conjecture (that is, one can replace the 0.2 with any number less than 1). In fact, he proved a considerably stronger statement: He showed that infinitely often q-p (ln q)^{8/9}. It seems clear that Goldston's work will have a profound and long-lasting impact on prime number theory, and some people believe that it can be used to prove a $3,000 conjecture of P. Erdos (although Erdos died a few years ago, you can still get money if you solve one of his prize problems) on large gaps between primes. Perhaps it will one day lead to the solution of the Twin Prime Conjecutre, or maybe even the Goldbach conjecture. Please do not email me.
1. Re:Goldston's Result by Anonymous Coward · 2003-03-30 13:04 · Score: 0
  
  It seems clear that Goldston's work will have a profound and long-lasting impact on prime number theory, and some people believe that it can be used to prove a $3,000 conjecture of P. Erdos
  
  I rather doubt it. Even if it got you as far as proving arbitrarily long arithmetic progressions of primes (a fantastic result and probably worth some prize money), it still wouldn't answer Erdos' $3000 conjecture which applies to ANY sequence of positive integers whose sum of reciprocals diverges.
There is a term for this... by Ayanami+Rei · 2003-03-30 10:40 · Score: 1

(and it's not "canceling out")

It's "undefined". When approaching the value of a function from different directions in the complex plane gives you different numbers, the value of the function there is called undefined. None of the points nearby line up, but it's not "in the middle", that would imply it switches direction and comes back down!!! (which it doesn't). So, we say that it just doesn't have a value in there. In fact, the domain of the function 1/x expressedly prohibits x to be zero, usually in math proofs you see something or other over x where x != 0. Just so that you don't forget. :-)

The fact that the concept of dividing by zero doesn't make sense to you is evidence for that! You know?

On the other hand, the directed limits THEMSELVES (i.e. the end of the pattern 1, 1/2, 1/3, 1/4, etc.) DO exist, and it's the obvious value (+inf. from the positive axis, -inf from the negative real axis, etc.). But this works because you aren't dividing by zero, but asking what the sequence is approaching. THAT is defined... it's evident from the series.

--
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
irrational != fractional by Ignominious+Cow+Herd · 2003-03-30 13:46 · Score: 1

Clearly you do not understand the meaning of the word 'irrational'. At least not in this context. Perhaps in some other context you do.

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Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.