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Prime Numbers Not So Random?

Posted by chrisd on 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."

26 of 147 comments (clear)

  1. anyone else getting the feeling... by ddd2k · · 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 ddd2k · · 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
    2. Re:anyone else getting the feeling... by farnsworth · · 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.

    3. Re:anyone else getting the feeling... by Yokaze · · 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"
    4. Re:anyone else getting the feeling... by Scarblac · · 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.
    5. Re:anyone else getting the feeling... by Scarblac · · 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.
    6. Re:anyone else getting the feeling... by KDan · · 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
    7. Re:anyone else getting the feeling... by Smidge204 · · 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=

    8. Re:anyone else getting the feeling... by Smidge204 · · Score: 2, Funny

      I suggest you upgrade your browser. Apparently it doesn't process the tag correctly.

      =Smidge=

  2. Encryption? by asdfx · · 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 itsme1234 · · 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. Cheh... but we already known it's not random by Red+Pointy+Tail · · 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.

  4. figure & ground by obtuse · · 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.
  5. Re:Immicibility gap by Anonymous Coward · · Score: 2, Funny

    You sir, are a liar. Physicists mix quite well.

  6. Here's the rub by Anonymous Coward · · 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 · · 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.

  7. I've got one! by Andy_R · · 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
  8. Re:I found a pattern! by itsme1234 · · 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.

  9. Anyone can test this theory out. by pauldy · · 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 · · 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.

  10. Skip right to the paper. by molo · · 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.
  11. Some numbers to look at by big_alpaca · · 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

  12. Unexpected Patterns of Diagonal Lines by chemstar · · 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.

  13. Re:Physicists pulling a cold fusion? by l2718 · · 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

  14. How to prove that all odd numbers are prime by dargaud · · 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 ?
  15. Re:Of course primes are nonrandom... by n1vux · · 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