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Any history of capitalism will start around the 1500s. Check it out yourself. Locke was on this shit at 1690 when he was publishing books such as "Some Considerations of the Consequences of Lowering of Interest, and Raising the Value of Money." Reference: [here] But google it up, theres lots of info on capitalism before the poster child Adam Smith appeared.

Prime Curios is indeed an interesting site.

It is believed (but not quite proven) that there is no highest prime.

Actually it is well proven that there are an infinite number of primes. Here is a really straightforward, simple proof.

Binary math has many special properties in group and number theory. We'd lose those in higher base math, and we wouldn't gain new properties to make up for that loss. Two, the low bound, is special.

Not sure what you mean here. Yes, groups of order 2 have some special properties, but so do groups of various prime and square orders etc. '2' is indeed a special prime, being the smallest absolutely, but that doesn't give it a monopoly on having special properties. See Here for some more resources on prime numbers (OK, now I really sounds like a geek.)

DeCSS Prime

Gallery of CSS Descramblers

sorry... but if you are arguing that perception of energy = "time", what things like about the regular rate of nuclear decay, the acceleration of mass due to gravity, which don't depend on any perceptions ?

I think you may be confusing the human experience with physics. Try reading some Kant, and perhaps Locke if you are interested in that topic. Also, check out why 60 hertz is important to human sight

sorry... but if you are arguing that perception of energy = "time", what things like about the regular rate of nuclear decay, the acceleration of mass due to gravity, which don't depend on any perceptions ?

I think you may be confusing the human experience with physics. Try reading some Kant, and perhaps Locke if you are interested in that topic. Also, check out why 60 hertz is important to human sight

Why is the number one not prime?

Hume

figured that out more then 200 years ago.
Why is science always the last to figure things out?

OOo is not a web browser.

Yes, I know (although it did, in the past, have a Web browser component). But the point is that my statement about OOo is a logical consequence of your claim that a standard's intent is irrelevant. In other words, if your irrelevance claim is true, then my OOo claim must be true. Therefore, if you do not accept the OOo claim, you cannot accept the irrelevance claim (unless you contest the deductive reasoning). This is an example of a reductio ad absurdum argument.

Notwithstanding this, if my words have come across as aggressive then you have my apologies. However, observe that I have attacked (at several places) your argument that Mozilla doesn't have superior standards support, and you have not presented counter-arguments to most of my responses, or any new reasons why your assertions are valid. They are therefore still in doubt, and hence you cannot claim to have "proven" your point.

see: here for proving primality and

here for some other interesting facts about primes.

Why do I point you to pages about primes, when you're talking about factoring? Well, the tests for primality and the tests for factors happen to be contrapositives, and so a particular test will find both--though certain properties about primes allow short-cuts that factoring won't allow.

see: here for proving primality and

here for some other interesting facts about primes.

Why do I point you to pages about primes, when you're talking about factoring? Well, the tests for primality and the tests for factors happen to be contrapositives, and so a particular test will find both--though certain properties about primes allow short-cuts that factoring won't allow.

According to the Prime Pages (http://www.utm.edu/research/primes/), the speed limit in Trenton, Tennessee is 31 miles per hour. A fondness for prime numbers? No - 31 miles per hour is very close to 50 kilometres per hour.

===

Conversion between mph and km/h is simple when you know the trick.

1 mile = 1.609344 km
Limit of ratio of successive terms in Fibonacci sequence ~= 1.618034

So for small numbers you can approximate by using the Fibonacci sequence: 5 miles is about 8 km, 8 miles is about 13 km, and so forth.

I suggest reading Searle's thought expirement "The Chinese Room", and more pointedly, criticisms of it.

Here is a good balanced approach to it.

Personally, I think it's just a glorified fallacy of composition.

Any packaged string can always be resampled from analog and move out into the wild.

This sort of thing is of great interest to me. The issues here are actually twofold. First is that some generic idea of "content" can be represented by multiple bit streams. Never mind resampling; how many different ways are there to encode a specific song? The combinations of different bit rates, different encoders, and different formats is staggering. Somehow, all those series of ones and zeros are going to be assigned (in theory) to the copyright holder? Maybe, but consider . . .

The second part of the problem is that a series of ones and zeros is meaningless without context. The decoding algorithm comes into play. What do you do if your nice new piece of software just happens to tar+gzip (or in some other way get encoded) into something that can be decoded, in whole or in part, by some music software to an mp3 of the latest manufactured band? It's like the illegal prime. Any laws that get passed regarding digital content without a lot of insight are going to leave things a real mess in the future.

Prime numbers are defined to be both integers and positive.

At least, that's what Eric Weisstein thinks.
So do The Prime Pages

Gotta be positive, por favor.

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.)

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.

I however, do not believe in the Big Bang or the new Sheets Theory...

Cosmology and biology are entirely different fields. Current theories of the development of the universe have very little, if anything, to do with the theory of evolution, and the evidence for the two types of theory are entirely independent. I should add that the philosophical issues at the bottom of each type of theory are also entirely different.

In the case of cosmology the philosophical question is something like "where did all the stuff that makes up the universe come from?" Traditionally the three available answers have been "from nothing" or "it has always been here", or "from God". Of course the God answer simply shifts the problem back one step to the question of "where did God come from?" Traditionally the two available answers have been "from nothing" and "he has always been here". See a pattern forming here? David Hume did, which led him somewhat sarcastically to suggest a third answer to the God question as well, namely "from a super-God".

In the case of biology the philosophical question is, roughly speaking, "how did all this biological stuff get so well organised?" Traditionally the only answer available was "God designed it that way" (Hume, as you might expect wanted to know how God got to be so well organised). The theory of evolution provides an answer to this philosophical problem. It shows how any structure that replicates can become better organised over time.

Whether you like the modern answers to the problems or not, my point here is just that they are different problems with different answers. You should not confuse your disagreement with one for disagreement with the other.

How could he go to his peers when they all seem to share your views about evolution?

This is the usual complaint of most cranks. The best answer is just to point out all the responses to his work that were not mere ridicule, but were careful explanations of why his arguments do not work, and why his factual claims are often false. A lot of biologists believe in God, and many more simply do not care whether God exists or not. If Behe's work had any scientific merit then there would be plenty of scientists to give it a fair hearing.

How do you propose the universe began?

I don't propose that the universe "began". I don't think it is the kind of thing that can have a begining, any more than a cicle can have a begining. I canot imagine how time could have an end. Why should I imagine that it had a start? But all of this is beside the point. The question of whether the universe came from has nothing to do with biology or the theory of evolution.

This argument is "Strong AI". Not all AI advocates this. There are many arguments against strong AI, one of which is Searle's Chinese Room.

As in Nicolo Machiavelli?

And yes, I first learned that name when my opponents in Sid Meir's Civilization called me Machiavellian.

There was an analysis written regarding the phrase "Life, Liberty and Persuit of Happiness" and it essential boiled down to this. Those words were chosen very specificaly and placed in the order that they were specificaly.

If I recall correctly, these words were actually a modification to philosopher John Locke's writings on human rights.

W

"No man's life, liberty, or property are safe while the legislature is in session." - Mark Twain

Think about the space required to store that many primes...your method of "trial division" is also known as "brute force".
Here is a very fast program that generates primes using the concept of Wheel factorization
Wheel factorization sounds like a neat way to factor composites, but I tried it and it cannot compare to the quadratic sieve or the number field sieve

Here it is in a link form.

No matter how smart you can make a computer look, it is still performing the same fetch-execute cycle on primitive instructions like "add," "shift," and "branch." If that is a conscious life form, then so is a pencil and piece of paper on which you perform all these primitive instructions manually.

Fan of John Searle, are you?

How's this for a thought experiment. Take a human being, and swap one of his neurons for an electronic circuit that behaves identically to a neuron. One at a time, swap out each real neuron and swap in an electronic one. Is he still concious when his brain is entirely made up of electronic neurons instead of organic ones? OK, now swap out each neuron, and swap in a tiny computer that can simulate the I/O behavior of a neuron. Swap these in one at a time. Is he still concious? OK, now start swapping out groups of neurons for computers that can simulate the I/O behavior of the group. Proceed until his entire brain is just one computer. When did he go from a human being to a soulless automaton?

...pre-Socratic philosophers did the same thing. Leucippus for example, was the first one to put forward the concept of atomism, and that was ~400 BCE.

The ideas are interesting by themselves, linking to other's work isn't much a validation in itself.

You mean this post doesn't rival the writings of Shakespeare or the thoughts of Aristotle?

Why, I belive it is genius rivalled only by Einstein.

I won't be happy until they air commercials on the TV of Illegal Prime Numbers

I hear if you use a lossy compression algorithm the number shrinks down to 42.

It a song by Tommy TuTone. Jenny's Phone #

(1) What Lamarck suggested is not Evolution in the sense it has today and
(2) Here are lots of examples of pre-Lamarckian evolutionary theories.

I'd reply, but I fail to see what your post has to do with mine...

I merely discussed the reasons for stiffer penalties againt violent street crime than white collar crime.

You went on a typical slashdot reduction ad absurdum against drug screening. I'm not seeing the connection.


---Lane

Why is C14 not valid for dates past what you gave? Because there is no C14 present!!!

O.k. so you don't understand what "half-life" means. Maybe you should familiarize yourself with the insigths of Zeno. Here's a quick refresher quiz and applet on half-life. The general idea is that by always taking half of something away, you will always have something left over.

Anyway, back to what I'm guessing is your point.

Why can't C14 be used for dates greater than about 5000 years? Because there is supposedly no C14 left!!!

From the information provided in the link your 5,000 years is missing a zero. It's used from samples up to 50-60K years old. There is sill C14 left at this point and there will be for a long time, such is the nature of half-life. It seems that it is not deemed accurate beyond this point.

So, if we take a sample that is supposedly 50,000,000 years old, then we would expect to find NO C14. Now, if we take this sample, and there is enough C14 to give us a date, then two things can be concluded:

It gives you a date, but it is not an accurate date.

1. The dates given by different methods do not agree with each other

Yes, especially after the useful period for C14 dating is passed.

2. The sample is perhaps much younger than previously thought

No, it is simply being measured by the wrong device. And so the nitpicking concludes.

Thanks. Great explanation.

Very kind of you to say, thanks.

Could you elaborate and tie this in with the number of primes between m and n?

I'm a little less confident about this, but here goes...

As I understand it (and bear in mind that I've not done any complex analysis for several years, and number theory has never really been my forte) sometime during the 19th century Gauss noticed that the distribution of primes was approximated pretty well by a function he called the `logarithmic integral'.

Li(x) is defined as the integral from 0 to x of (1/t) dt. And apparently the number of primes below x (usually denoted pi(x)) is pretty well approximated by Li(x).

Now this is where I start to lose track of things.
As I understand it, it was proved at the beginning of the 20th century that the validity of the Riemann hypothesis is equivalent to the assertion that the deviation of Li(x) from the actual value of pi(x) is of the order of sqrt(x)*ln(x).

If I remember correctly, some work of the three great British mathematicians Hardy, Littlewood, and Hardy-Littlewood showed that pi(x) actually oscillates around Li(x) infinitely many times (although it really doesn't do it very quickly - the first value of x for which the graphs cross is very big indeed).

qv: the Clay Institute's page
and Chris Caldwell's page for better explanations.

As to whether there's a relatively simple proof out there, I don't know. My (non-specialist) suspicion is that there isn't, because some really clever people have tried to find one for a century and a half and failed. I'd be interested and impressed to be proved wrong on this, though.

Andrew Wiles' celebrated proof of Fermat's Last Theorem (if you haven't done so, read Simon Singh's book on the subject, and if possible watch the BBC Horizon documentary - the transcript is available) was pretty complicated and, I'm told (algebraic geometry isn't my field either - there's an awful lot of diverse mathematics out there) introduced some genuinely new ideas and methods.

The general feeling is that if there were a simple proof of either Fermat or Riemann (or, for that matter, the Goldbach or Poincare Conjectures) then someone would have found it by now - some really top brains have worked on all of these over the years (including several Fields medallists, FRSes, and the like).

(There's a guy who posts regularly to sci.math who reckons he's got a simple proof of Fermat which doesn't resort to all that scary stuff about elliptic curves or modular forms. The consensus seems to be that he's a nutter, though - his `proofs' contain obvious flaws which he refuses to acknowledge, claiming instead the existence of an enormous academic conspiracy against his work.)

It's also often the case (and this was true for the Fermat theorem) that proofs of such intractible problems, even those which are subtly flawed, introduce new ideas and methods of attack.

This is why otherwise sensible mathematicians have a go at these problems - even if they don't manage to solve them, the chances are that the attempt will inspire them to find new methods or potentially important partial results. Even had Wiles' original (flawed) proof turned out to be irrepairable, it was a pretty major piece of work which introduced some important new ideas which could well be useful in solving related problems.

My guess (as an interested non-specialist) is that while a proof of RH would be complicated and elegant, it would also involve some new twist or idea. As for who might do it, my money would be on Prof Louis de Branges of Purdue University - he demolished the (similarly intractible) Bieberbach Conjecture in the 1980s and thus seems to know what he's doing. Or it might be someone else entirely, someone who's spent seven years locked in their attic (as Wiles did).

nicholas

As it's not what *I* concluded, I'm not sure why you mention it. What I *did* provide was objective evidence that peer review is not the only way of progress in science. As But every example you offer indicates the strength of the peer review process

One example (Margulis) relates to peer review. I am not so sure that 10 years for the field to move from open derision to acceptance is a 'strength' however both sides of that coin are value judgements. My statement is not that peer review doesn't work, rather that 'there's more than one way to do it'.

What use is it if a lone wolf "gets it right", if we can't tell that he/she got it right?

In the instances I quoted you can tell when they make something that works. The market is not a perfect peer-review but it's a darned efficient one.

Poincare could not have ... Quantum Mechanics did not even begin to exist until the discovery of the electron in 1897

How 'bout you take it up with the author of: Poincare,'s proof of the quantum discontinuity of nature. - Jeffrey J. Prentis; 63 (4), 339-50.

As it happens Poincare's 3-body problem is also seen as the first consideration of the chaotic systems which are part of Wolfram's departure from the mainstream.

I will grant that Poincare saw a lot of the implications of non-Euclidean spaces, a fundament of Einstein's General Relativity

How kind of you. Poincare is 'acknowledged as a co-discoverer, with Albert Einstein and Hendrik Lorentz , of the special theory of relativity'

To close on some of the problems which I do see in the practice of modern academic science in general and peer review in particular:

• Peer review engenders:
• thousands of academic journals each of which can be subscribed to at a cost of $250-1000/ year
• a body of knowlege which is substantially disjoint from the knowlege of 'technology'
• a view at Nature, one of the pre-eminent publications that their few hundred words of review of ANKOS is worth $15 to me

In 2001, a 4 million decimal-digit number was proven to be prime. This is a single-bit result, but reaching it had taken 2 years of spare computing cycles on 205,000 computers (or something like that). That's a very expensive bit.

http://www.mersenne.org/13466917.htm

http://www.utm.edu/research/primes/notes/13466917/

No, the worst typ of theft is when they use an illegal number.
That's really low!
Why should the public be allowed to use copyrighted or otherwise proprietory numbers?
It's not like numbers should be free, free numbers would DESTROY THE ECONOMY!
Think of the children!

First, 25 is not a perfect number (see http://primes.utm.edu/glossary/page.php/PerfectNum ber.html).
Second, the original poster (the one whose age is a perfect number and about to be a prime) is, I'm guessing, 28 years old and is almost 29.

• Sounds fine to me. Trouble with your hypothesis is, controlled experiments aren't required for the scientific method.

Very interesting. I had always thought that controlled experiments were required for the Scientific Method. I may have been mistaken.

It seems that this source suggests that systemized observations are at the core of the Scientific Method as first laid out by Francis Bacon.

I said before that those who are unwilling or unable to perform experiments are not Scientists. Perhaps a better formulation is those who are unwilling to do experiments are not Scientists. I'm sure Astrophysicists would love to be able to experiment, and perhaps, who knows, one day they will.

Homeopaths and the like have antipathy toward experimentation at all. I think we can guess why this is.

Perhaps I shouldn't have allowed my distaste for Social Scientists to bleed over into fields like Biology and Astrophysics.

And, perhaps I should study my terms more thoroughly before I start ranting.

Thanks.

Where's the fun in that? We already know those prime numbers exist!

i think the point of the search is that some 2^x-1 are prime, and some are not... and because of the mathematics involved, it is relatively easily to factor them, and to also find some really huge primes in the process...

the deeper question of why the heck we should look for them are more philosophical... some concrete reasons? there are cryptological applications, i think, and mathematical implications, most definitely... but mostly, it's just kewl, you know? why do anything in life? why go to the south pole? why go to mars? why get out of bed in the morning!

here's a good list of detailed reasons:
Tradition!
For the by-products of the quest
People collect rare and beautiful items
For the glory!
To test the hardware
To learn more about their distribution

The public domain has several issues.

• It means the content is not copyrighted. Either the copyright has expired, or was released.
• Lack of copyright is not equivelant to a lack of liability.
• There are implied warranties and liabilities for particular uses when other areas of law are applied. Liability and warranties are not limited to copyright.
• Any change, even minor, creates a 'derivative work' of the PD work, allowing anyone to usurp the work you have done.
• The user of PD content must be able to PROVE that the content is available as public domain.

Decoders for various image, movie, and disc formats have been released into the public domain, yet the authors have been sued or had lawsuits filed against them. This is a case that lack of copyright does not mean lack of liability. Take DeCSS for a single example of that.

On the other hand, products released under the GPL have very specific rights granted and released.

• Authors maintain the copyright
• Distribution of the program distributes all the GPL rights.
• There is absolutly no warranty or liability for any use, as far as is allowed by law.
• Patents based on content in GPL software must be licensed for everyone's free use, or not at all.
• Redistribution must follow specific rules, or it is prohibited

First a case where a GPL'd program could generate an infringing program. Observe that in the case of DeCSS, it COULD NOT be released under GPL because portions of the content are patented, and the patent owners are unwilling to agree to that style of license issue. The program CAN be released to the Public Domain, because the author does not need to keep the copyright. The legality of the program is being decided by the courts.

A perfectly legal GPL'd prime number generating program could generate the DeCSS source code as a prime number which is illigal under the DMCA. The program has substantial non-infringing uses, but is also clearly punishable by the DMCA. Granted, the author of a PD prime-number generator is could probably make the same arguments as the GPLed software arguments. The GPL explicitly disclaims all liability provided the conditions are met (which a prime number generator does).

Gigalaw's copyright permission myths page states:

Public domain only refers to the lack of copyright protection. While copyright is very important, a work may be protected by other legal theories that survive after the copyright expires. For example, public domain artwork, particularly distinctive characters (such as Beatrix Potter's "Peter Rabbit" illustration), can achieve protection under trademark law and function as a logo or source identifier. Likewise, mere ideas, which are not protected under copyright law, may be protected under trade secret or contract law.

For more information on the GPL's philosophy, check out the Gnu/FSF philosophy page.

---
The ideas expressed are not necessarily those of anyone, including myself.

Related link: DeCSS prime number

I have friends who work in the security industry and crack codes for a living. Every time a watermarking scheme is publically proposed, they laugh long and heartily. The simple fact of the matter is that a system designed to check for a watermark can easily be changed to invalidate the watermark. Watermarks are necessarily little bit-flipping programs that don't alter the outward appearance of the media they are attached to, so what makes record execs and PHBs so sure that they can't be removed?

The only watermark that can't be removed is the watermark that can't be detected. And that doesn't help the digital rights management fascists one bit. So why do they bother?

Well, they still think it's a "deterrent." Just like Macrovision is a "deterrent" when you can buy filters to block it for under $25 on eBay. Sooner or later, though, the world is going to have to learn that information wants to be free, that trying to restrict the flow of bits on the information superhighway is futile, and that selling simple numbers and calling it "property" is patently absurd. Mathematics is a part of nature, and nobody owns nature; the sooner our laws are brought into line with this simple truth, the better.

~wally

I'm not sure how this sort of philosophical moral relativism can be adequately defended. The actions were immoral -- it doesn't matter if he planned it from the beginning or not.

Its as if I had a bank account for 10 years at the local bank before I knocked it off instead of the guy who wandered into town one day and held it up. Its still a bank robbery. Maybe one would make a better made-for-tv movie than the other though.

-Michael
Take a hike! Go to http://www.mtnhike.com

Since I've seen posts from at least one kernel developer in response to the attached story, I figured that this might be a good place to ask the following question:

A little while ago, I wrote an application that uses an incredible amount of memory... A very space inefficient implementation of Eratosthenes' Sieve. In essence, what the algorithm does is cycle through the entire contents of memory sequentially many, many times (not a completely correct description). What I found with the following three kernel versions:

• 2.4.4
• 2.4.8
• 2.4.17

My question for the Kernel gods out there is as follows: are there any stable 2.4.x kernel releases out there that would handle this type of stress without the performance degradation that I've experienced with these kernels?

" . . . futility of war . . . . "

War can be considered many things, but it is not futile. All we are, and all we believe is the result of thousands of years of warfare--the "winning" side promoting their agenda [religion, philosophy, genetic code, or business] and destroying/assimilating the "losing" population.

To quote the cliché, "History is written by the victor".

To this end, war is not "futile"--this is not an evaluation of whether war is "right", "justifiable", or "a necessary evil". Regardless of these [important] evaluations, war is effective.

That's part of the reason it's a problem.

There is a certain futility to modern warfare. In that, war requires deeds now considered unethical in most cultures; great contradictions as "Thou shalt not kill" and Ste. Augustine's "Just War".

What is making modern war futile [thankfully] is our problem with executing it properly. A typical pre-industrial culture has different rules of war--take the Japanese, Aztecs, Native Americans, Cossacks--the general rule is, conquer them by slaughter, kill all of their men, kill all of their children down to the cradle, rape/marry/kill all of their females so their decedents are also yours. If you applied this method to Palestine or Ireland, there would not be a terrorist problem in either location.

This method was applied by the Europeans and their American, Canadian, and Mexican decedents upon the scores of nations in the Americas [at least we gained the "United Nations" idea from the Iroquois nations first]. How many terrorist attacks have occurred based upon an entire continent under occupation? Close to none over the last hundred years.

Also, war seemed effective in eliminating slavery in the USA. And, through allowing the slave-owning population to survive, resulted in a very powerful terrorist organisation to be born [the KKK]. Strong enough to have both Senators and Governors as open members for about a century.

So, we are unwilling to fight these kinds of wars anymore, and follow the logical course--we start making the war "clean". Higher technology does not mean "more ethically sound" war. The United States has the military-industrial power to nuke just about any nation on Earth into molten glass, and then gave flotillas of B-52s dumping salt to cover their entire land so that nothing grows there for a thousand years. But instead of using the higher-tech to build more effective weaponry in greater quantities, they develop highly precise weaponry and invent the concept of "surgical strikes".

But don't think that it'll just be a bot-on-bot match. The end targets are the same--military, industrial, command and control, logistic, support, and 'terror'. All of which involve people. If the Taliban/Al-Qaeda had the capacity to pop up a sub of nuke-wielding bots in San Francisco, you wouldn't be stretching to find the "suffering of war".

What's really changed:
Tech-war results in much fewer civilian casualties, especially when you consider the numbers and agendas involved.
Modern warfare is ineffectual against occupying areas and halting ideas.

Since Orwell was quoted to start, I'll quote him to close:

People sleep peaceably in their beds at night only because
rough men stand ready to do violence on their behalf.
--George Orwell

It has been done lots of times. Based upon chromosomal organization here and based upon DNA sequences here, for example or here for a good set of lecture notes on the topic.

After the 23rd Mersenne prime was found at the University of Illinois, the mathematics department was so proud that they had their postage meter changed to stamp "2^11213-1 is prime" on each envelope.

Does anyone have an envelope with this stamp on it?

Well I feel, not to be redundant, that this was a very good decision. Having free speech win out over every other law in the land is a good thing. Besides, how can you outlaw a prime number?

• Intelligence can depend on the environment: Is a spider intelligent? Spining a web it's amazing, stick the thing in a bath tub and it doesn't look so smart.
• Intelligence can be social: is an ant intelligent? Not by itself but ant colonies perform some pretty amazing feats.
• Intelligence may depend on other knowledge: A chess grandmaster may play a very strange move near the beginning of the game which looses him the game. Why? He took a calculated risk and it didn't pay off. Was he dumb? No, you say. What if it wasn't a chess grandmaster but Joe Blogss from down the street - yeah THAT was a dumb move...

Regarding the second point - this gets to the heart of the Chinese Room Argument: can intelligence (I would distinguish "sentience") be "built" or "must" there be something more. Was deep blue intelligent? Searle would argue "no". Some would argue "Yes, In the chess domain". There was nobody on the planet it couldn't teach somethign about chess and (to an extent) explain those choices. Many AI researchers weren't happy about deep blue because it basically used very fast search and no fancy reasoning. But hey - that just shows that there's more than one way to solve a problem IMHO...

ah, found a good link on probable primes (used for RSA etc): http://www.utm.edu/research/primes/notes/prp_prob. html

What did you expect? We're living in a democracy. It doesn't mean things will be OK, or even acceptable. It means that the country is (ideally) ruled by the majority of the people.
So what we get is the dictatorship of the majority. Most people are stupid, so they deserve stupid laws. They even deserve a stupid president. Just too bad nobody recognizes the joke is on them.

Socrates said the same thing in the Apology. Despite Plato and Socrates dislike for democracies, there are some nice words in Plato's Republic book 8 about democracy.

Basically paraphrased, democracy is the worst form of government (rule by the ignorant), however it provides the most freedom