"I know whereof I speak, "... "the number 4.56106531 would be rounded to 4 in the "nearest even" case"
You are nothing but a long-winded bullshitter, spouting crap. Your up-moderations are utterly undeserved.
But then again, those I know familiar with NA always call it "nearest or even", whoever decided to elide such an important word from the name should be shot.
One extra syllable and the world would have been spared your misinformation.
PHP is an utter abomination. It's turned into what it was trying to contrast itself against (something with the complexity of Perl). It's been designed by committee, and is now a camel with 5 humps.
(Curious aside - did you know that the Norwegian for giraffe is literally "periscope horse"?)
Anyway, you're dead right, JS, even though it's usually programmed by complete idiots for completely idiotic purposes, is far better designed - by competent computer linguists, than PHP.
And I know PHP is popular (some of my contracts have been PHP, some people just seem to think the sun shines out of its back end) so I'll get flamed for the above, but fork it - I've got Karma to burn!
Currently, I expect SoB to be the only project to better their record.
If normalised score is a good measure of a project's size, and capability for finding huge primes, which I believe it is for most projects (which is why I invented the concept in the first place), then the reasons for this expectation become clear:
<URL:http://primes.utm.edu/bios/top20.php?type=pro ject&by=ScoreNormal> <<< 6517719 Great Internet Mersenne Prime Search 199552 Seventeen or Bust 14285 Yves Gallot's GFN Search Project 5195 Riesel Sieve Project 3390 Prime Internet Eisenstein Search 2031 12121 Search 1219 15k*2^n-1 search 1182 The Prime Sierpinski Problem... >>>
As the score for a prime with n digits is proportional to n^3.log(n), we can see that Yves' GFN project, even if it were up to full speed, which it isn't, is 13th the size of SoB. Thus it's only sensibly cabable of finding primes of about 42% of the size at a similar rate to SoB. The rest of us, basically, are nobodies!
Of course, SoB have set themselves a very tricky target. However, that trickiness is one of the things that causes their family of primes to grow in size quite dramatically, if they can keep the CPU input high. It could easily be that they only find two or three more primes due to this incredible growth - the larger ones will just be out of reach to current types of technology. I hope not though.
One thing that might surprise you is the fact that JavaScript is possible the most powerful of all. It's got all of the features that you list.
You're not a real JavaScript programmer until you've Curried functions in it! (Though the variadic nature makes the construct not as neat as in the purer functional languages.)
I cannot speak for the EFF. But I do know several people directly involved with the administration of those awards, and have discussed many topics with them.
The smaller prizes - 1M digit (already awarded), and 10M digits (still pending) are actually pretty small and unimportant. They can be attacked simply by throwing huge numbers of inexpensive commodity PCs at the task. That's basically what GIMPS is. The larger prizes are the important ones, as they reward a much harder achievement. The algorithms used to tackle such tasks don't scale particularly well. It's more than 10 times harder to do a problem 10 times bigger. This in part is because of the hierarchical memory system that PCs have. Small fast caches, other medium-sized slower caches, and then large quantities of relatively slow main memory. FFTs really don't like such a hierarchical memory architecture, as they grab data from all over the place all of the time. Caches become very hard to use effectively, and enormous L1 caches are prohibitively expensive.
So these later prizes will almost certainly be awarded to systems either based on new algorithms that are vastly more scalable than current FFTs, or on new hardware (memory) designs which somehow get around the caching issue.
Moving up to even larger sizes, it may become impractical to perform such calculations on a single PC. Therefore communications systems will want to be invented that provide no more latency than main memory.
Those are real concrete advances in computer technology, and it's those that are being rewarded. The primes are almost a red herring.
Sophie Germain was a female who made important advances in number theory, inparticular to do with prime numbers (and Fermat's Last Theorem).
When this prime: http://primes.utm.edu/primes/page.php?id=20278 885817959*2^24712-1 was found, several years ago, it was something like the 7th largest known Sophie Germain prime in the world. The finder, like Sophie, was female. Both were and are utterly devoid of (their own) penis.
Alas it's no longer one of the top-20 Sophie Germains, but time marches on at a frightening rate, and primes are growing at an amazing rate: http://primes.utm.edu/top20/sizes.php
Let Phi(n,x) be the n-th cyclotomic polynomial evaluated at x. Therefore Mersenne primes are Phi(p,2) for some p. I found the prime Phi(98304,1063662)=1063662^32768-1063662^16384+1 the other day. However, it is _tiny_ with only 197000 digits (something like the 240th largest in the world).
Lots of people are finding large prime numbers - if you find one over ~64000 digits, it'll be one of the largest 5000 known primes. See http://primepages.org/
They've missed several very important PCs - ones from the equally keen, equally inventive, but smaller, UK market.
Where are Clive Sinclair's ZX80 (1st PC < #100), ZX81, ZX Spectrum, and QL (cheapest of the 4 68k machines)? TI rebranded some of those in the US, I know.
Where was the BBC Electron, Model A, and Model B. And the Acorn Archimedes with the ARM processor. A processor so well designed that pretty much every single other micorprocessor manufacturer has licensed its design (TI, Intel, Motorola, etc., etc.). I know the Beeb reached the US as my g/f had one when she was growing up.
It mentions Wing Commander, but has conveniently forgotten that WC was just/Elite/, the classic BBC game (and Spectrum and C64) on steroids.
And why is the era of the 20 address bit PC, and the 32-bit register 24-bit address space ST/Amiga/Mac/QL called the "16 bit era"? The 6502 and Z80 machines were the heyday of the 16-bit era. The fact that shitty PCs had a shitty OS was the "oh my god, 16-bit legacy refuses to die" era.
I dunno, but I remember 'mars.exe' (or was is mars.com?) from about 1993 or 1994. It was about 5k in size. If the author hadn't unrolled the loops fully, it would have been about 2k in size!
Utterly offtopic, but were you aware that the etymology of then and then is identical. They were, in early English, the same word. It's only chance that they ended up being clearly distinct in more recent times.
""" But compared to a 1024 bit RSA key (which has somewhere around 2^128 valid keys), you'd have to do 2^112 iterations. """
Erm. in 1024-bit RSA, then you may have as many as 2^1023 valid keys. (As if {p,q}~=2^512, then phi(pq)~=2^1024, and almost all {d,e}<phi(pq) are coprime to phi(pq) (so only even numbers are guaranteed to be excluded, hence the division by 2)
Shor himself doesn't believe his eponymous algorithm will ever be practical. See his usenet posts from the last decade. IIRC, he's said that he doesn't believe QC will be practical, and thus his algorithm will never have a platform to run on.
Re random bits - they're only as perfect as your measurement of a right angle. However, it's pretty easy to unbias nearly random independent bits, so that's not a show stopper. FP.
No, the bits have a property that is shared between their endpoints. If you insert 2 more endpoints in the middle, then the original enpoints no longer have the shared property. The first thing that Alice and Bob do is to check that they have the shared property on a small set of the bits, and thus an evesdropper will be detected immediately.
It's a bit more complicated than that, but the essential thing is to note that it's impossible to duplicate a quantum state. Once you've read it, you've extracted one bit of information from it, but the original contained more than one bit of information. Therefore the MITM can't reproduce what he was sent, merely what he read, which is different 50% of the time.
I wrote a obfuscated self-modifying perl script which would let you play with such a scheme. Alas it requires some knowledge of how the scheme works in order to use it.
If the algorithm or source code aren't publicly available, then it's probably security through obscurity. Kerchoffs law, and all that.
In the end of the day, you can't beat rubber-hose cryptography, buxom-blonde cryptography, or photos-at-the-seedy-gay-bar cryptography -- they'll crack even the strongest protocol.
"Whichever one of the AWK trio who first explored the heuristics of regular expressions."
I was going to suggest "one of Aho, Sethi, Ullman" for writing the Dragon book, to which every modern sensible language owes a great debt. (Don't ask what I consider to be 'sensible' though!)
So it looks like Aho has 2 partial votes at least!
One of the better multi-lingual automatic translators I've seen did actually use Esperanto as the backbone. Esperanto has a very limited vocabulary, and perhaps this works in its favour, as it was never a 1-1 word mapping, but a word->phrase mapping. In English, there's usually a word, sometimes several, that are "close enough", and one of those gets picked as being the translation, losing many nuances that could be carried if phrases were permitted.
I've not checked, but perhaps 'jewelry' is the word they're missing. Jewelry doesn't have to be made with jewels nowadays (e.g. wooden jewelry is not uncommon).
Slashdot Mirror
"I know whereof I speak, " ...
"the number 4.56106531 would be rounded to 4 in the "nearest even" case"
You are nothing but a long-winded bullshitter, spouting crap.
Your up-moderations are utterly undeserved.
But then again, those I know familiar with NA always call it "nearest or even",
whoever decided to elide such an important word from the name should be shot.
One extra syllable and the world would have been spared your misinformation.
You're confusing "with arbitrary results" with "with arbitrary precision".
PHP is an utter abomination. It's turned into what it was trying to contrast itself against (something with the complexity of Perl). It's been designed by committee, and is now a camel with 5 humps.
(Curious aside - did you know that the Norwegian for giraffe is literally "periscope horse"?)
Anyway, you're dead right, JS, even though it's usually programmed by complete idiots for completely idiotic purposes, is far better designed - by competent computer linguists, than PHP.
And I know PHP is popular (some of my contracts have been PHP, some people just seem to think the sun shines out of its back end) so I'll get flamed for the above, but fork it - I've got Karma to burn!
Currently, I expect SoB to be the only project to better their record.
o ject&by=ScoreNormal> ...
If normalised score is a good measure of a project's size, and capability for finding huge primes, which I believe it is for most projects (which is why I invented the concept in the first place), then the reasons for this expectation become clear:
<URL:http://primes.utm.edu/bios/top20.php?type=pr
<<<
6517719 Great Internet Mersenne Prime Search
199552 Seventeen or Bust
14285 Yves Gallot's GFN Search Project
5195 Riesel Sieve Project
3390 Prime Internet Eisenstein Search
2031 12121 Search
1219 15k*2^n-1 search
1182 The Prime Sierpinski Problem
>>>
As the score for a prime with n digits is proportional to n^3.log(n), we can see that Yves' GFN project, even if it were up to full speed, which it isn't, is 13th the size of SoB. Thus it's only sensibly cabable of finding primes of about 42% of the size at a similar rate to SoB. The rest of us, basically, are nobodies!
Of course, SoB have set themselves a very tricky target. However, that trickiness is one of the things that causes their family of primes to grow in size quite dramatically, if they can keep the CPU input high. It could easily be that they only find two or three more primes due to this incredible growth - the larger ones will just be out of reach to current types of technology. I hope not though.
One thing that might surprise you is the fact that JavaScript is possible the most powerful of all. It's got all of the features that you list.
You're not a real JavaScript programmer until you've Curried functions in it! (Though the variadic nature makes the construct not as neat as in the purer functional languages.)
I cannot speak for the EFF. But I do know several people directly involved with the administration of those awards, and have discussed many topics with them.
The smaller prizes - 1M digit (already awarded), and 10M digits (still pending) are actually pretty small and unimportant. They can be attacked simply by throwing huge numbers of inexpensive commodity PCs at the task. That's basically what GIMPS is. The larger prizes are the important ones, as they reward a much harder achievement. The algorithms used to tackle such tasks don't scale particularly well. It's more than 10 times harder to do a problem 10 times bigger. This in part is because of the hierarchical memory system that PCs have. Small fast caches, other medium-sized slower caches, and then large quantities of relatively slow main memory. FFTs really don't like such a hierarchical memory architecture, as they grab data from all over the place all of the time. Caches become very hard to use effectively, and enormous L1 caches are prohibitively expensive.
So these later prizes will almost certainly be awarded to systems either based on new algorithms that are vastly more scalable than current FFTs, or on new hardware (memory) designs which somehow get around the caching issue.
Moving up to even larger sizes, it may become impractical to perform such calculations on a single PC. Therefore communications systems will want to be invented that provide no more latency than main memory.
Those are real concrete advances in computer technology, and it's those that are being rewarded. The primes are almost a red herring.
Sophie Germain was a female who made important advances in number theory, inparticular to do with prime numbers (and Fermat's Last Theorem).
When this prime:
http://primes.utm.edu/primes/page.php?id=20278 885817959*2^24712-1
was found, several years ago, it was something like the 7th largest known Sophie Germain prime in the world. The finder, like Sophie, was female. Both were and are utterly devoid of (their own) penis.
Alas it's no longer one of the top-20 Sophie Germains, but time marches on at a frightening rate, and primes are growing at an amazing rate:
http://primes.utm.edu/top20/sizes.php
Brute forcing is not the simplest technique to attack the Number-Theoretic based Public Key algorithms, and never will be.
Therefore negligible changes to brute force techniques produce less than negligible (that's zero) change to how one attacks such algorithms.
Your wish is my command.
Let Phi(n,x) be the n-th cyclotomic polynomial evaluated at x.
Therefore Mersenne primes are Phi(p,2) for some p.
I found the prime Phi(98304,1063662)=1063662^32768-1063662^16384+1 the other day. However, it is _tiny_ with only 197000 digits (something like the 240th largest in the world).
Lots of people are finding large prime numbers - if you find one over ~64000 digits, it'll be one of the largest 5000 known primes.
See http://primepages.org/
But it played chess! 1KB and it bloody beat me every time!
Lousy article, 2/10 if I'm generous.
/Elite/, the classic BBC game (and Spectrum and C64) on steroids.
They've missed several very important PCs - ones from the equally keen, equally inventive, but smaller, UK market.
Where are Clive Sinclair's ZX80 (1st PC < #100), ZX81, ZX Spectrum, and QL (cheapest of the 4 68k machines)? TI rebranded some of those in the US, I know.
Where was the BBC Electron, Model A, and Model B. And the Acorn Archimedes with the ARM processor. A processor so well designed that pretty much every single other micorprocessor manufacturer has licensed its design (TI, Intel, Motorola, etc., etc.). I know the Beeb reached the US as my g/f had one when she was growing up.
It mentions Wing Commander, but has conveniently forgotten that WC was just
And why is the era of the 20 address bit PC, and the 32-bit register 24-bit address space ST/Amiga/Mac/QL called the "16 bit era"? The 6502 and Z80 machines were the heyday of the 16-bit era. The fact that shitty PCs had a shitty OS was the "oh my god, 16-bit legacy refuses to die" era.
I dunno, but I remember 'mars.exe' (or was is mars.com?) from
about 1993 or 1994. It was about 5k in size. If the author
hadn't unrolled the loops fully, it would have been about 2k
in size!
Back when coding was real coding...
Excellent place for a typo, grand-dad.
Utterly offtopic, but were you aware that the etymology of
then and then is identical. They were, in early English, the
same word. It's only chance that they ended up being clearly
distinct in more recent times.
Read up on Kanada's super-computer pi-calculating exploits.
The state of the art is nearly 2 generations beyond anything that is done on PCs.
Hey - could we get those headlines to blink too? That would be cool!
FP.
"""
But compared to a 1024 bit RSA key (which has somewhere around 2^128 valid keys), you'd have to do 2^112 iterations.
"""
Erm. in 1024-bit RSA, then you may have as many as 2^1023 valid keys. (As if {p,q}~=2^512, then phi(pq)~=2^1024, and almost all {d,e}<phi(pq) are coprime to phi(pq) (so only even numbers are guaranteed to be excluded, hence the division by 2)
FP.
Shor himself doesn't believe his eponymous algorithm will ever be practical. See his usenet posts from the last decade.
IIRC, he's said that he doesn't believe QC will be practical, and thus his algorithm will never have a platform to run on.
FP.
Holey moley, oops. I just said what you said.
I should get some sleep...
Re random bits - they're only as perfect as your measurement of a right angle. However, it's pretty easy to unbias nearly random independent bits, so that's not a show stopper.
FP.
No, the bits have a property that is shared between their endpoints. If you insert 2 more endpoints in the middle, then
the original enpoints no longer have the shared property.
The first thing that Alice and Bob do is to check that they
have the shared property on a small set of the bits, and thus an evesdropper will be detected immediately.
It's a bit more complicated than that, but the essential thing is to note that it's impossible to duplicate a quantum state. Once you've read it, you've extracted one bit of information from it, but the original contained more than one bit of information. Therefore the MITM can't reproduce what he was sent, merely what he read, which is different 50% of the time.
I wrote a obfuscated self-modifying perl script which would let you play with such a scheme. Alas it requires some knowledge of how the scheme works in order to use it.
If the algorithm or source code aren't publicly available, then it's probably security through obscurity. Kerchoffs law, and all that.
In the end of the day, you can't beat rubber-hose cryptography, buxom-blonde cryptography, or photos-at-the-seedy-gay-bar cryptography -- they'll crack even the strongest protocol.
FP.
"Whichever one of the AWK trio who first explored the heuristics of regular expressions."
I was going to suggest "one of Aho, Sethi, Ullman" for writing the Dragon book, to which every modern sensible language owes a great debt. (Don't ask what I consider to be 'sensible' though!)
So it looks like Aho has 2 partial votes at least!
FP.
One of the better multi-lingual automatic translators I've seen did actually use Esperanto as the backbone. Esperanto has a very limited vocabulary, and perhaps this works in its favour, as it was never a 1-1 word mapping, but a word->phrase mapping. In English, there's usually a word, sometimes several, that are "close enough", and one of those gets picked as being the translation, losing many nuances that could be carried if phrases were permitted.
I've not checked, but perhaps 'jewelry' is the word they're missing. Jewelry doesn't have to be made with jewels nowadays (e.g. wooden jewelry is not uncommon).
Phil
I go you take the car this evening?
???
Going should take the infinitive, not the 2nd person singular.
It's certainly not good French - it's barely French at all.
FP.