If the solution scales exponentially with the size of the problem, then it is no solution. Exponential complexity of all known algorithms is the very fact that makes NP-hard problems intractable.
Using the word NP in the title is damnable sensationalism, suggesting that progress has been made on theoretical computer science's biggest open problem when in fact the article has no bearing on NP-completeness at all.
Maybe they can go after the person who distributes the file creation recipe. But that person is, at worst, guilty of contributory infringement.
The beauty of xor is, that nobody can be sued for direct infringement.
I understand that sueing for contributory infringement is not easy. For example, you need to send formal (and hence expensive) takedown notice before you can do anything. It may therefore only practical when dealing with massive infringers.
The xor method is indeed very good, I wonder why it has not yet been used by filesharing networks? (My guess: it is too expensive to generate high quality random files of the necessary size. Also it doubles b/w requirements).
It reminds me of the legal conundrum where identical twins commit two different murders at the same time but in different places. There are plenty of witnesses, but the police can't be sure who killed whom. The two murder cases get assigned to two different judges. Will the twins go free? (Variation: the victims are the twins).
You are indeed as far off base as can be. Every file is a sequence of bits which is a number already.
And prime numbers are notoriously hard. That's why they are used in encryption, whose goal is kind of opposite, namely to make extraction as hard as possible.
A good approximation to pi(x), the number of all primes below x, which was first given by Gauss is obtained by taking as starting point the empirical fact that the frequency of prime numbers near a very large number x is almost exactly 1/log x. From this, the number of prime numbers up to x is approximately given by the logarithmic sum
Ls(x) = 1/log 2 + 1/log 3 +... + 1/log x
which can be bounded from below by x/log x.
So, if x has 1400 digits, the number of primes below x will have 1397 digits, give or take one.
So you could save three bytes. Surely a contender for the prize for the most gratuitous use of all cpu time until the end of time.
so what makes this one special? Is it an important theorem, is it beautiful, will it help with the discovery of further theorems? Does it solve a well-known open problem?
"Now named the Klehr-Bliss theorem" named by whom? Are other mathematicians talking about it?
Obviously, the reporter knows nothing. Why, then, should we even read this uninformed chatter?
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If the solution scales exponentially with the size of the problem, then it is no solution. Exponential complexity of all known algorithms is the very fact that makes NP-hard problems intractable. Using the word NP in the title is damnable sensationalism, suggesting that progress has been made on theoretical computer science's biggest open problem when in fact the article has no bearing on NP-completeness at all.
All science is either physics or stamp collecting (said Ernest Rutherford)
Maybe they can go after the person who distributes the file creation recipe. But that person is, at worst, guilty of contributory infringement. The beauty of xor is, that nobody can be sued for direct infringement. I understand that sueing for contributory infringement is not easy. For example, you need to send formal (and hence expensive) takedown notice before you can do anything. It may therefore only practical when dealing with massive infringers.
The xor method is indeed very good, I wonder why it has not yet been used by filesharing networks? (My guess: it is too expensive to generate high quality random files of the necessary size. Also it doubles b/w requirements).
It reminds me of the legal conundrum where identical twins commit two different murders at the same time but in different places. There are plenty of witnesses, but the police can't be sure who killed whom. The two murder cases get assigned to two different judges. Will the twins go free? (Variation: the victims are the twins).
You are indeed as far off base as can be. Every file is a sequence of bits which is a number already. And prime numbers are notoriously hard. That's why they are used in encryption, whose goal is kind of opposite, namely to make extraction as hard as possible.
A good approximation to pi(x), the number of all primes below x, which was first given by Gauss is obtained by taking as starting point the empirical fact that the frequency of prime numbers near a very large number x is almost exactly 1/log x. From this, the number of prime numbers up to x is approximately given by the logarithmic sum Ls(x) = 1/log 2 + 1/log 3 + ... + 1/log x
which can be bounded from below by x/log x.
So, if x has 1400 digits, the number of primes below x will have 1397 digits, give or take one.
So you could save three bytes. Surely a contender for the prize for the most gratuitous use of all cpu time until the end of time.
so what makes this one special? Is it an important theorem, is it beautiful, will it help with the discovery of further theorems? Does it solve a well-known open problem? "Now named the Klehr-Bliss theorem" named by whom? Are other mathematicians talking about it? Obviously, the reporter knows nothing. Why, then, should we even read this uninformed chatter?