Prime Numbers Not So Random? 147
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."
anyone else getting the feeling... (Score:4, Interesting)
Re:anyone else getting the feeling... (Score:1, Funny)
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 notewo
Re:anyone else getting the feeling... (Score:2, Insightful)
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.
Re:anyone else getting the feeling... (Score:1, Insightful)
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 r
Re:anyone else getting the feeling... (Score:1)
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?
Re:anyone else getting the feeling... (Score:1)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:4, Insightful)
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".
Re:anyone else getting the feeling... (Score:2)
> 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".
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:4, 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 [everything2.com]
Proof that e is irrational: http://everything2.com/index.pl?node_id=930313 [everything2.com]
Better examples are obviously out there, but I just searched for 'irrational' on E2... You're very ignorant.
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2, Informative)
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
Re:anyone else getting the feeling... (Score:5, 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=
Re:anyone else getting the feeling... (Score:1)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:2, Funny)
=Smidge=
Re:anyone else getting the feeling... (Score:1)
"2 is prime, 4 is prime, 6 is prime, 8 is prime..."
Re:anyone else getting the feeling... (Score:2)
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.
Re:anyone else getting the feeling... (Score:3, Funny)
In English, you can easily use real grammar and real words. On slashdot, however, you are on your own.
Re:anyone else getting the feeling... (Score:2, Interesting)
Re:anyone else getting the feeling... (Score:2)
Re:anyone else getting the feeling... (Score:1)
Re:anyone else getting the feeling... (Score:3, 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 theor
Re:anyone else getting the feeling... (Score:1)
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 i
Re:anyone else getting the feeling... (Score:2)
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 constructe
Re:anyone else getting the feeling... (Score:2)
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 la
Re:anyone else getting the feeling... (Score:1)
Like this? [pnl.gov].
Took about 30 seconds with google, and that's because I misspelled Pythagorean. Good thread, however.
Re:anyone else getting the feeling... (Score:1)
Of course it's possible. Between high school, college, and grad school I'm sure I proved hundreds of propositions about infinite sets.
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
Re:anyone else getting the feeling... (Score:2)
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 happ
Re:anyone else getting the feeling... (Score:2)
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.
Encryption? (Score:3, Informative)
Re:Encryption? (Score:2, Insightful)
Next step is to ask: "will my Diesel car become obsolete because of this theory" ?
Re:Encryption? (Score:2)
Daniel
Re:Encryption? (Score:1)
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.
Re:Encryption? (Score:2)
Oh, and from what I've seen, it does take
Re:Encryption? (Score:2)
Daniel
Cheh... but we already known it's not random (Score:2, Funny)
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.
figure & ground (Score:4, Interesting)
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.
Re:figure & ground (Score:1)
Re:figure & ground (Score:2)
Uh, hello? 2?
That's just a measuring error :-)
Re:figure & ground (Score: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?
Re:figure & ground (Score:1)
Re:figure & ground (Score:2)
Re:figure & ground (Score:2)
Unless you're not seeing the posts to which I've been replying.
Re:figure & ground (Score:2)
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)
Re:figure & ground (Score:2)
Re:the undefined-ness of division by zero (Score:2)
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.
Re:Cheh... but we already known it's not random (Score:1)
Re:Cheh... but we already known it's not random (Score:2)
Re:Cheh... but we already known it's not random (Score:1)
That is a big jump for him/her! Consider this moderator obviously comes from elementary grade.
Physicists pulling a cold fusion? (Score:2)
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?
Re:Physicists pulling a cold fusion? (Score:2)
Re:Physicists pulling a cold fusion? (Score:3, Informative)
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 (onl
Re:Physicists pulling a cold fusion? (Score:1)
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
Here's the rub (Score:5, Interesting)
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.
Re:Here's the rub (Score:3, Informative)
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.
Re:Here's the rub (Score:2)
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 tha
They mostly share a quality (Score:2)
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,
Re:They mostly share a quality (Score:1)
results of your script:
Sorry :-)
I've got one! (Score:3, Funny)
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
Re:I've got one! (Score:2)
Re:I've got one! (Score:1)
Re:Here's the rub (Score:2)
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.
Re:Here's the rub (Score:1)
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?
Re:Here's the rub (Score:2)
A non trivial formula, you mean. Otherwise the following applies:
P(x) = 7(x/x)
The pattern ... (Score:1)
I found a pattern! (Score:2)
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!
Re:I found a pattern! (Score:2)
So not a prime.
Daniel
Re:I found a pattern! (Score:2)
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 tr
Re:I found a pattern! (Score:2)
Re:I found a pattern! (Score:5, Insightful)
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.
Re:I found a pattern! (Score:1)
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.
Re:I found a pattern! (Score:2)
Yes! Fields Medal! Now!! Before I get too old for it...
Re:I found a pattern! (Score:2)
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 (..
Re:I found a pattern! (Score:1)
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.
Re:I found a pattern! (Score:1)
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 pr
Anyone can test this theory out. (Score:3, Interesting)
Re:Anyone can test this theory out. (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.
Re:Anyone can test this theory out. (Score:2)
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 clueles
vapid... (Score:1)
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" (Score:1, Interesting)
Perhaps these guys should map out their sequences of prime number differences to see if it generates a picture ?
Parallels with Lem's "His Master's Voice" (Score:2)
Skip right to the paper. (Score:3, Informative)
Information Entropy and Correlations in Prime Numbers -- Abstract [lanl.gov]
Information Entropy and Correlations in Prime Numbers [PDF] [lanl.gov]
Information Entropy and Correlations in Prime Numbers [Postscript] [lanl.gov]
-molo
Re:Skip right to the paper. (Score:2)
Re:Skip right to the paper. (Score:2)
-molo
Some numbers to look at (Score:2, Interesting)
Unexpected Patterns of Diagonal Lines (Score:2, Informative)
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
11:15, restate my assumptions (Score:1)
2*2*
Of course primes are nonrandom... (Score:2)
Randomness is not actually entropy.
--Dan
Re:Of course primes are nonrandom... (Score:2, Informative)
The pattern they've found is a logarithmic distribution, it seems, according to their abs
They're all over the place ... (Score:1)
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.
F
How to prove that all odd numbers are prime (Score:5, Funny)
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 ...
Most common prime in nature? (Score:1)
Re:How to prove that all odd numbers are prime (Score:2)
Re:Immicibility gap (Score:2, Funny)
You sir, are a liar. Physicists mix quite well [mchawking.com].