As the old proof goes, to demonstrate that there are an infinite number of primes: Multiply the first N primes together then add 1 - the result is a number not previously divisible by any of the first N primes.
But that doesn't mean it's prime.
My reasoning - why doesn't that also hold for "multiply the first N primes together then SUBTRACT 1", with the notable exception of "1" as that's only divisible by itself.
It does hold - you do end up with another number which is not divisible by any of the first N primes. But, again, that doesn't make it a prime.
What do you mean, "no"? The article already posited "2" as the hoped for answer, which doesn't make sense as an answer to your question. Also what's with using a double-character name for your variable? Crazy.
The stated proof assumes the new number is prime. This is not a valid assumption.
Isn't it, at least under the stated conditions? The assumption that the new number is prime is made because it is not divisible by any of the supposedly complete set of primes used in its construction. I don't quite see why you need to add the "...or it is composite" to complete the reductio ad absurdum*.
*which is either what they told me proof by contradiction is called in Latin, or something Harry Potter was taught in Transfiguration.
means that that the gaps between consecutive numbers don't keep growing forever.
What I see now is that it really means that while gaps can (and presumably do) keep to a general trend of growth, there will always be a gap of less than 70 million somewhere up ahead.
There are (infinitely many) prime numbers for which you'll find another one within 70 million, but it's not true for every prime number
Nope, it is true. Consider only the prime pairs. There are, we now know, no gaps larger than 70 million. Add the rest of the prime numbers and there can still be no gaps larger than 70 million.
just another way to make poor people that can't afford adequate representation into criminals
Really? And there's me thinking it was an effort to stop them committing more crimes. Or is there a reason "they" want more criminals?
when they shouldn't be.
Which in this case of a DUI means having a BAC under 0.0x%, an objective measurement determined by a calibrated machine. Hell, over here they'll even give you a ride to the police station if you blow over and give you the choice of blowing into an even more accurate machine (twice, lowest score counts) or taking a blood test, so you've got plenty of opportunity to objectively prove your legal innocence before it gets anywhere near a court.
Since what constitutes "offensive" material varies wildly from person to person and also depending on the reason/motives people have to do any particular search, I doubt there is any way for autocomplete to comply.
That's why we have a lot of objective*, if necessarily somewhat arbitrary, laws, and courts to mete out punishment when someone breaks them. It wouldn't really work if you had one party claiming they'd been wronged by their own standards and the other party just disagreeing and being done with it.
*that's the idea, anyway, but lawyers have to put food on the table somehow.
I bet the plaintiff would consider my post defending autocomplete's cluenessless offensive.
Offensive to him, perhaps - but he certainly wouldn't get very far claiming it was defamation, which is what he's claiming of autocomplete, and is a different thing.
Then you can prosecute them for driving like an idiot, if you've got that evidence. But DUI stands for "Driving Under the Influence" - it's not "Driving Under the Influence but also noticeably driving badly," and it's on the books because drunk drivers might well be capable of driving themselves along the familiar route from the local pub to their home without raising an eyebrow from a passing cop, and yet still hit a child who ran out into the road whom they might otherwise have avoided had they not been intoxicated, among myriad other scenarios.
Or would you be happy to let anyone behind the wheel as long as they don't look like they're wasted once they're driving?
How about simply ban DUI checkpoints.
Once they're no longer effective at detecting and discouraging drink-driving, sure. We can even disband the police altogether once crime has been eliminated, if you like.
Horrible. Drunk driving laws should be based on how a person is driving, not an arbitrary level on a meter that isn't tied to an individuals ability to drive.
And how do you determine how impaired a driver is, in anything but an arbitrary way? One driver's reaction times may be shot to hell, yet he can still drive straight and at speed. Another may we be weaving, but still able to avoid colliding with stationary objects. If we didn't have arbitrary legal limits on such things the lawyers would see to it that every case took six years and a billion dollars to pursue.
often, not always, the crime is victimless.
I could say the same about closing my eyes and firing randomly into a 100-seater auditorium with five people in it.
The DUI laws, while well intentioned, are a huge source of revenue for the criminal "justice" system
So deny them the revenue. It shouldn't be hard to do.
You can't really measure something arbitrary like drunkeness with a simple blood test.
No, but you can sure as hell get the cases through the courts - or even to the courts - a lot quicker. It is, like so many laws, the arbitrary but useful line in the sand.
That's what I came here to ask. It sounded like bullshit:
“Error level analysis (ELA) works by intentionally resaving the image at a known error rate, such as 95%, and then computing the difference between the images. If there is virtually no change, then the cell has reached its local minima for error at that quality level. However, if there is a large amount of change, then the pixels are not at their local minima and are effectively original.”
Slashdot Mirror
This isn't rigorous, but my view:
Conjectures don't stand or fall on "views".
As the old proof goes, to demonstrate that there are an infinite number of primes: Multiply the first N primes together then add 1 - the result is a number not previously divisible by any of the first N primes.
But that doesn't mean it's prime.
My reasoning - why doesn't that also hold for "multiply the first N primes together then SUBTRACT 1", with the notable exception of "1" as that's only divisible by itself.
It does hold - you do end up with another number which is not divisible by any of the first N primes. But, again, that doesn't make it a prime.
I'm also wondering what "impact" means here. "Indirectly impact" doubly so.
Well, yes, that's exactly what this is. Which is what the summary says.
What do you mean, "no"? The article already posited "2" as the hoped for answer, which doesn't make sense as an answer to your question. Also what's with using a double-character name for your variable? Crazy.
You could always help me out and explain it to me - if you have a point to make - instead of being a condescending dick.
The stated proof assumes the new number is prime. This is not a valid assumption.
Isn't it, at least under the stated conditions? The assumption that the new number is prime is made because it is not divisible by any of the supposedly complete set of primes used in its construction. I don't quite see why you need to add the "...or it is composite" to complete the reductio ad absurdum*.
*which is either what they told me proof by contradiction is called in Latin, or something Harry Potter was taught in Transfiguration.
Researchers hoping to get '2' as the answer
In case anyone's as confused as I was, I think I've finally figured out The Question, which is:
What is the smallest gap between consecutive primes which occurs infinitely many times?
Or something like that. Everyone thinks it's probably 2.
means that that the gaps between consecutive numbers don't keep growing forever.
What I see now is that it really means that while gaps can (and presumably do) keep to a general trend of growth, there will always be a gap of less than 70 million somewhere up ahead.
finds that there are infinitely many pairs of primes that are less than 70 million units apart.
Doh. I read "pairs of primes" as "twin primes" - as in pairs of twin primes less than 70 million apart.
Why are you so upset that a lot of people enjoy it? No-one's having a go at you for not liking it.
Timothy Lord... Tim Lord... Timmy Lord... Tim E. Lord...
Oh god. I just had a horrible thought about the big reveal coming up in Saturday's episode.
There are (infinitely many) prime numbers for which you'll find another one within 70 million, but it's not true for every prime number
Nope, it is true. Consider only the prime pairs. There are, we now know, no gaps larger than 70 million. Add the rest of the prime numbers and there can still be no gaps larger than 70 million.
Now add one to X. Now add one to X.
Oops. Just add one, not two ones. Two shalt thou not add.
Or the number is divisible by a prime that wasn't in you initial set.
GP has already used all the supposed finite number of prime numbers in constructing his contradictory bigger prime.
The US are getting it late, it seems.
Isn't that getting to be often the way? One might naively assume it was some kind of desperate ploy to defeat piracy...
The only country that got Iron Man 3 after the USA (so far) was Poland.
just another way to make poor people that can't afford adequate representation into criminals
Really? And there's me thinking it was an effort to stop them committing more crimes. Or is there a reason "they" want more criminals?
when they shouldn't be.
Which in this case of a DUI means having a BAC under 0.0x%, an objective measurement determined by a calibrated machine. Hell, over here they'll even give you a ride to the police station if you blow over and give you the choice of blowing into an even more accurate machine (twice, lowest score counts) or taking a blood test, so you've got plenty of opportunity to objectively prove your legal innocence before it gets anywhere near a court.
Since what constitutes "offensive" material varies wildly from person to person and also depending on the reason/motives people have to do any particular search, I doubt there is any way for autocomplete to comply.
That's why we have a lot of objective*, if necessarily somewhat arbitrary, laws, and courts to mete out punishment when someone breaks them. It wouldn't really work if you had one party claiming they'd been wronged by their own standards and the other party just disagreeing and being done with it.
*that's the idea, anyway, but lawyers have to put food on the table somehow.
I bet the plaintiff would consider my post defending autocomplete's cluenessless offensive.
Offensive to him, perhaps - but he certainly wouldn't get very far claiming it was defamation, which is what he's claiming of autocomplete, and is a different thing.
The timing is no coincidence; Star Trek: Into Darkness is coming out on Friday.
Awesome! Uh, except that I already saw it last Friday...
Video evidence would be driving like an idiot:
Then you can prosecute them for driving like an idiot, if you've got that evidence. But DUI stands for "Driving Under the Influence" - it's not "Driving Under the Influence but also noticeably driving badly," and it's on the books because drunk drivers might well be capable of driving themselves along the familiar route from the local pub to their home without raising an eyebrow from a passing cop, and yet still hit a child who ran out into the road whom they might otherwise have avoided had they not been intoxicated, among myriad other scenarios.
Or would you be happy to let anyone behind the wheel as long as they don't look like they're wasted once they're driving?
How about simply ban DUI checkpoints.
Once they're no longer effective at detecting and discouraging drink-driving, sure. We can even disband the police altogether once crime has been eliminated, if you like.
Horrible. Drunk driving laws should be based on how a person is driving, not an arbitrary level on a meter that isn't tied to an individuals ability to drive.
And how do you determine how impaired a driver is, in anything but an arbitrary way? One driver's reaction times may be shot to hell, yet he can still drive straight and at speed. Another may we be weaving, but still able to avoid colliding with stationary objects. If we didn't have arbitrary legal limits on such things the lawyers would see to it that every case took six years and a billion dollars to pursue.
often, not always, the crime is victimless.
I could say the same about closing my eyes and firing randomly into a 100-seater auditorium with five people in it.
The DUI laws, while well intentioned, are a huge source of revenue for the criminal "justice" system
So deny them the revenue. It shouldn't be hard to do.
You can't really measure something arbitrary like drunkeness with a simple blood test.
No, but you can sure as hell get the cases through the courts - or even to the courts - a lot quicker. It is, like so many laws, the arbitrary but useful line in the sand.
You're not. Especially when the first "improvement" to be mentioned is "the addition of multiple social providers."
Improvements include the addition of multiple social providers on the desktop
On the desktop? Don't you mean "on the side of the Firefox window"?
“Error level analysis (ELA) works by intentionally resaving the image at a known error rate, such as 95%, and then computing the difference between the images. If there is virtually no change, then the cell has reached its local minima for error at that quality level. However, if there is a large amount of change, then the pixels are not at their local minima and are effectively original.”
Why can't a RAW image be faked?