Indeed, the number of particles in the universe is assumed to be approximately 10^85, so if you would store one bit per particle, you'd need about 5*10^530 universes to store all those primes. Hell, even if you stored at every single particle as many bits as there are particles in the universe, you'd still need 5*10^445 universes.
Of course that's assuming you stupidly write all those numbers individually down, using the whole 2048 bitf or each number. Now what if we compress the table?
The complete list can, of course, be stored in a bitfield with 2^2048 individual bits which tell if a given number is prime or not (e.g. 1 means the number is prime, 0 means it's not). Now, of those 3.23*10^616 bits, about 2.27*10^613 bits are 1. So a simple approximation would be to treat the bits as independent, with each one having a probability of (2.27*10^613)/(3.23*10^616)=7.03*10^-4 of being 1. So if we neglect all correlations of the bits, we get an information of about 0.0084 bits per bitfield bit, which means we can compress to about 2.7*10^614 bits. That is, even neglecting all correlations (even the trivial ones of all even numbers except 2 being non-prime) we get only about 12 bits per prime. That's substantially less than the 2048 bits per prime we'd need with straightforward storage. Of course, we would still need an insane number of universes to store our table:-)
Now, of course we know that we can "compress" the full table very well to a small prime-finding program which fits nicely on even a single floppy (but would take longer to "decompress" than we are willing to wait), so the list of primes doesn't actually contain too much information (indeed, the program can compress the whole infinite prime table - decompression of course needs unlimited ressources, then -, therefore the average information content of a single prime is obviously zero).
Given that lots of extensions work in Mozilla as well (like Tabbrowsing extension, Adblock, mouse gestures), which extensions are Firefox-only?
Re:Convert friends - add top 10 reasons for FF her
on
Firefox 1.0 Released
·
· Score: 1
About 2: The way you described it it's a reason to write standards conforming web pages, not a reason to use Firefox: What advantage do Firefox users have from the fact that standard conforming web pages (which they don't create, but browse) also show up in other browsers?
No, the point to make is that standard conforming web pages display correctly in FireFox (well, as long as you don't hit the "slashdot bug"...). Whereas IE doesn't even fully implement CSS1.
If you refer to the left column overlapping with the main one, the following workaround works for me with Mozilla; maybe it works with Firefox as well:
Step 1: Change your font size (it doesn't matter to what, just that it's different than the original). Step 2: Change back to the original font size.
After that procedure, the overlap magically disappears (at least as long as you don't go to another page). The fastest way to get this is to type Ctrl-Plus, then Ctrl-Minus.
Well, maybe that explains why we have continents which do not cover all of Earth's surface? (Reminder: The sea floor is a different material than the continents!)
Well, solar energy (and all those derived from it, like wind energy or water energy) isn't renewable as well. It's based on the remaining hydrogen in the sun, and the sun will die after that is used. Of course, it's quite a while until then, and it will happen whether we use that energy or not, besides the fact that at that time the earth will be doomed anyway, but hey, it's not a renewable energy source!
Why? After all, isn't it nice to be able to say: There exists an uniquely determined pair of siamese twin primes. BTW, there's only one golden mean as well, and it still has a name!:-)
Well, the power lasted just for very short time (remember, he couldn't even get back because he didn't have the energy; he had to utilize a flash for that).
In the first place? From supernova explosions. Fortunately we don't need to hunt for supernovae, since past supernove products are stored near the surface of our planet:-)
Europe isn't as homogeneous in this question as your post implies. While France is very pro-nuclear, the German government decided to get out of nuclear power during the next 30 years or so. And Austria never used nuclear power at all (although they built a nuclear power plant, but it never went online due to political reasons).
For me, the best ISP is the one I notice the least. Basically, I want a reliable pipe to the internet, for as little cost as possible. Nothing more and nothing less.
Since the gap between two primes cannot get smaller than the gap between 2 and 3 (i.e. no number in between at all), the minimum gap is actually a constant function as soon as you passed 3 (and undefined before, of course).
Now, giben that primes with only one number in between are called twin primes, what about 2 and 3, which are even closer, with nothing in between? Maybe siamese twin primes?
Slashdot Mirror
Or to state it shorter:
There's a difference between copying and plagiarism.
You forgot the integrated operating system.
You might think that
- Profit
would be even more efficient, but I've tried it and it didn't work at all.Well, it always depends on the market you take as base.
:-)
I guess Firefox has 100% of the Firefox market.
Or to the Riemann zeta function, which gives the interesting relation:
The sum over all positive integer n of 1/n^s is the same as the product over all prime numbers p of 1/(1-p^-s).
Indeed, the number of particles in the universe is assumed to be approximately 10^85, so if you would store one bit per particle, you'd need about 5*10^530 universes to store all those primes. Hell, even if you stored at every single particle as many bits as there are particles in the universe, you'd still need 5*10^445 universes.
:-)
Of course that's assuming you stupidly write all those numbers individually down, using the whole 2048 bitf or each number. Now what if we compress the table?
The complete list can, of course, be stored in a bitfield with 2^2048 individual bits which tell if a given number is prime or not (e.g. 1 means the number is prime, 0 means it's not). Now, of those 3.23*10^616 bits, about 2.27*10^613 bits are 1. So a simple approximation would be to treat the bits as independent, with each one having a probability of (2.27*10^613)/(3.23*10^616)=7.03*10^-4 of being 1. So if we neglect all correlations of the bits, we get an information of about 0.0084 bits per bitfield bit, which means we can compress to about 2.7*10^614 bits. That is, even neglecting all correlations (even the trivial ones of all even numbers except 2 being non-prime) we get only about 12 bits per prime. That's substantially less than the 2048 bits per prime we'd need with straightforward storage. Of course, we would still need an insane number of universes to store our table
Now, of course we know that we can "compress" the full table very well to a small prime-finding program which fits nicely on even a single floppy (but would take longer to "decompress" than we are willing to wait), so the list of primes doesn't actually contain too much information (indeed, the program can compress the whole infinite prime table - decompression of course needs unlimited ressources, then -, therefore the average information content of a single prime is obviously zero).
To get a story at slashdot, of course.
...
Of course there are also some less important uses in programs like pgp or ssh
Given that lots of extensions work in Mozilla as well (like Tabbrowsing extension, Adblock, mouse gestures), which extensions are Firefox-only?
About 2: The way you described it it's a reason to write standards conforming web pages, not a reason to use Firefox: What advantage do Firefox users have from the fact that standard conforming web pages (which they don't create, but browse) also show up in other browsers?
...). Whereas IE doesn't even fully implement CSS1.
No, the point to make is that standard conforming web pages display correctly in FireFox (well, as long as you don't hit the "slashdot bug"
If you refer to the left column overlapping with the main one, the following workaround works for me with Mozilla; maybe it works with Firefox as well:
Step 1: Change your font size (it doesn't matter to what, just that it's different than the original).
Step 2: Change back to the original font size.
After that procedure, the overlap magically disappears (at least as long as you don't go to another page). The fastest way to get this is to type Ctrl-Plus, then Ctrl-Minus.
Yes, but that did cost them a lot more money.
Well, maybe that explains why we have continents which do not cover all of Earth's surface? (Reminder: The sea floor is a different material than the continents!)
Maybe I can get a patent on the business method of obfuscating patent descriptions in order to get granted trivial patents, err, I mean:
... :-)
Method to create material of patentable kind out of material of unpatentable kind by applying complexifying linguistic transformations.
Ok, maybe I should have another round of obfuscation^Wlinguistic transformation before submission
On Soviet Slashdot, the article title sounds suspiciously like YOU!
Such as yourself?
:-)
Why does the name "Brian" come to my mind?
It will be even more interesting if the electronics fails the other way: Imagine an error which makes your gun shoot when you didn't intend it to ...
Well, solar energy (and all those derived from it, like wind energy or water energy) isn't renewable as well. It's based on the remaining hydrogen in the sun, and the sun will die after that is used. Of course, it's quite a while until then, and it will happen whether we use that energy or not, besides the fact that at that time the earth will be doomed anyway, but hey, it's not a renewable energy source!
Why? After all, isn't it nice to be able to say: :-)
There exists an uniquely determined pair of siamese twin primes.
BTW, there's only one golden mean as well, and it still has a name!
Well, the power lasted just for very short time (remember, he couldn't even get back because he didn't have the energy; he had to utilize a flash for that).
In the first place? From supernova explosions. Fortunately we don't need to hunt for supernovae, since past supernove products are stored near the surface of our planet :-)
Europe isn't as homogeneous in this question as your post implies. While France is very pro-nuclear, the German government decided to get out of nuclear power during the next 30 years or so. And Austria never used nuclear power at all (although they built a nuclear power plant, but it never went online due to political reasons).
Maybe on hydrogen fuel cells, with the hydrogen produced with the energy from the nuclear plants?
For me, the best ISP is the one I notice the least. Basically, I want a reliable pipe to the internet, for as little cost as possible. Nothing more and nothing less.
Since the gap between two primes cannot get smaller than the gap between 2 and 3 (i.e. no number in between at all), the minimum gap is actually a constant function as soon as you passed 3 (and undefined before, of course).
Now, giben that primes with only one number in between are called twin primes, what about 2 and 3, which are even closer, with nothing in between? Maybe siamese twin primes?
Well, be glad that you didn't play Minesweeper ...