I cannot directly answer your claim about no studies being published that show smoking is harmless because I haven't read the literature but any reasonably competent researcher could write a paper showing that smoking might be harmless.
The problem with smoking is that the effects happen over a long term and there are many confounding factors to take into account - smokers often have a worse diet for example. At the end of the day the correlation of smoking with harm is the only one that stands up to extended scrutiny but it's not something that can be (easily) proved in a single study.
Bicycle helmet wearing rates are positively correlated with cyclist head injury rates. Countries (and states) that have introduced mandatory helmets have typically seen an increase in head injury rates after the introduction of the law unless the law was not enforced.
But you can find plenty of papers published that suggest that bicycle helmets prevent head injury. I don't know of any that say that bicycle helmet wearing is more dangerous than not (despite the correlation above) although there are also plenty that suggest that there is no net benefit to cycle helmet wearing and there are some that say that the reduction in cycling of mandatory helmet laws have a net deleterious health effect.
Bicycle helmet wearing efficacy testing is hampered by confounding factors. Just as one example, it has been measured that cars pass helmeted cyclists closer than unhelmeted cyclists. My nearest "miss" was being clipped on the arm by the wing mirror of a very fast moving car. I might not be alive today if I'd been wearing a helmet and he'd been two inches closer.
So you cannot just test a helmet in the lab and say that in event A, a helmet is better than no helmet because the frequency of event A might itself depend on the presence or absence of a helmet.
Harla Branno (mayor of Terminus) Vasilia Aliena (Dr Falstoffs daughter and by all accounts, one of the most brilliant roboticists on Aurora) Susan Calvin (The Einstein of robotics - still remembered hundreds of years later on a world that considers Earthmen to be little more than monkeys)
Good grief. Have you even read the wikipedia page, let alone the book itself?
From the wiki page:
"The philosophical problem is about the decrease in knowledge when it comes to rare events as these are not visible in past samples and therefore require a strong a priori, or an extrapolating theory; accordingly, predictions of events depend more and more on theories when their probability is small. In the fourth quadrant, knowledge is both uncertain and consequences are large, requiring more robustness."
There has never been as rapid a rise of CO2 as is happening now. The rare event that is happening now is not visible in the geological record.
We started to understand the greenhouse effect way back in the 1850s. By the 1920s we had the knowledge to completely understand it and the data was collected to verify it all by the 1950s.
We've built excellent models for predicting the long term behaviour of the climate due to the CO2 forcings we've introduced. Even the early models from the 1970s predictions have held up to scrutiny and later models are better still. If anything, the various models have tended to underestimate the changes to the climate.
When we extrapolate the current models the potential costs are absolutely catastrophic. In the worst cases it's hard to see how civilization can survive and even human extinction isn't inconceivable. If we'd started mitigating strategies in the 80s it might have cost us a tiny fraction of growth but we chose not to and every year we wait the evidence that we must act gets stronger and the costs higher.
And you're saying that "well we don't completely understand absolutely everything so we should continue running headlong to where the majority of scientists say there is a cliff to fall off" and then you quote a book that says that financial experts tend to underestimate the downsides due to incomplete knowledge as support for your inane views.
I don't know anything at all about German tax law but assuming it's even moderately like the UK then I don't understand why any of this is a surprise.
In the UK you are potentially liable for tax for all gains. Usually it will either be income tax or capital gains tax and as a general rule of thumb, if you buy something at one price with the intention of selling it at a different price it will be CGT while if you "earn" it it will be IT.
Bitcoin mining is an oddity because you don't buy the coins but produce them and I don't know where it falls but I would guess CGT but electricity costs etc would be deductible from any profit before tax was due.
There's an additional 10K allowance per year for CGT and you don't have to report gains below this so most people buying and selling shares for example don't really have to think about it.
Your only or main home is a significant exception where no CGT is payable (nor losses claimable). There are other exceptions - wine, cars.
Also selling things you no longer need is exempt from CGT (again, both for profit and loss) so selling stuff on ebay when you're having a clear out does not involve HMRC but trading (i.e. buying stuff with the intention of selling it again) will do.
On the whole I'd say the UK taxation system is fair and predictable. There are anachronisms - for example, if you jointly own a house with someone who isn't your spouse then any rental income/loss can be apportioned to either party in any proportion (you must let the tax office know the proportion if it doesn't match the ownership proportion) while if you are married then it must be apportioned either 50/50 or in the same proportion as the ownership is shared. Transfers between husband and wife are not reportable for CGT because gains and losses are not crystalized at the point of transfer so the gain is still taxable once the asset is finally disposed of. Capital gains are payable when they are realized - so if you make a 100K gain once in ten years then you will pay tax on 90K in the year you make the gain while if you can crystalize 10K per year you will pay no CGT (i.e. unused CGT allowances cannot be rolled forward) but if you make a big loss in one year then you can roll that forward so that future profits are not taxed until you've made up the loss.
There's a certain amount of effort to harmonize EU tax rules between countries. I would be surprised if the tax laws in Germany were very different - apart from anything else, if they were significantly different I'd have expected to see news reports about people taking advantage of the tax differences between UK and DE.
I suspect you're wrong. The average intelligence hasn't really changed much at all.
What has changed is what you're prepared to accept.
When you were 16, the fact that she was pretty and appeared to like you was more than sufficient to keep your interest in her (at least for a while)
Now you're finding that looks aren't nearly enough to keep your interest beyond the first time she opens her mouth.
Give it another ten years and you'll come to realize that looks really don't matter that much at all. You can admire the hot sexy ones from a distance while listening to the intelligent interesting ones. In time you might discover that she's pretty hot and sexy as well as interesting and intelligent - especially if she starts showing more than a social interest in you - and even if you don't you'll have found a new friend.
On the whole I find women more interesting, easier to talk to, and more intelligent than men.
This is a very contrived example that I've hacked together to show the possibly unanticipated problems of using auto and, in particular, changing code that has types explicitly coded to use auto instead:
#include <iostream>
class PublicClass {
private:
class PrivateClass {
public:
int i_;
int j_;
public:
void i_am_a() { std::cout << "I am a PrivateClass with values " << i_ << " and " << j_ << std::endl; }
PrivateClass(int i, int j):i_(i), j_(j) { }
operator PublicClass() { return PublicClass(i_+j_); }
};
int i_;
public:
PublicClass(int i):i_(i) { }
void i_am_a() { std::cout << "I am a PublicClass with value " << i_ << std::endl; }
PrivateClass operator+(const PublicClass& v) { return PrivateClass(i_, v.i_); } };
int main(void) {
PublicClass v1(4);
PublicClass v2(6);
PublicClass result = v1 + v2;
auto autoresult = v1 + v2;
// PublicClass::PrivateClass presult = v1 + v2;/* Does not compile */
result.i_am_a();
autoresult.i_am_a(); }
$ g++ -std=c++0x -o auto auto.cpp $./auto I am a PublicClass with value 10 I am a PrivateClass with values 4 and 6 $
I mean the new "auto" syntax is clearly just *designed* for job interview pedants rather than making the life of the everyday C++ programmer less tedious and error prone.
char c = 4; What is the type and value of the following expression? c + 2
While I like the new auto syntax I'm a little scared about having to deduce what the type is when incompetent programmers start using auto because they don't know what the correct type should be.
Much like my heart sinks when I see code using void* to store and pass pointers around and then cast them when they arrive at their destination.
In one codebase (a few tens of thousands of lines) I was tasked with addressing all the intermittent and unreproducible problems. More than 90% of the bugs were revealed just by replacing the void* with a pointer to the type that was actually being held, removing the casts, and then fixing whatever the compiler barfed on when there were incompatible types.
This is an enhancement because it never occurred to anybody to even attempt to do this during development and it never occurred to anyone that it would be attempted.
It's a bit like saying - well my car has wheel nuts so I can take the wheels off - and so I should be able to drive it with the wheels off and the fix we're now talking about is stopping you starting the engine while the wheels are off.
Something similar happens at the BBC Proms whenever there's a piano concerto.
The leader of the orchestra plays an A and then the prommers at the front applaud (This is just the done thing, like shouting "Heave" when the lid of the piano is opened - to which the gallery reply "Ho".) Sometimes the leader takes a bow, sometimes they just ignore it.
But sometimes the applause grows to the point where half the hall is clapping (but not the prommers who started it all)
You are right that in theory you can be a market maker without clearing but true market makers are members of the exchange. Being a market maker gives them certain extra freedoms and certain extra obligations.
And being a member of the exchange means that you get clearing.
It's not easy to predict what might happen if there wasn't true market makers.
Johnny wants to buy an apple at up to 49p. Chris wants to sell an apple at no less than 52p.
They're both sitting there doing nothing.
Flash the wonder trader decides that Johnny and Chris are both prepared to negotiate by up to 2p on what they say is their best offer. So Flash the wonder trader puts in a bid of 50p and an ask of 51p. This, because it's a better offer, sits ahead of both Chris's and Johnny's trades. Johnny decides that while Chris's 52p wasn't good enough, he'll take Flash's 51p offer to sell and Chris decides that while Johnny's 49p wasn't good enough, Flash's 50p offer to buy is good enough.
Flash pockets the 1p and he's happy.
Note that Flash can actually make the market work - Both Johnny and Chris are sitting there unwilling to make the first move towards a compromise - each is thinking that if they move first then the other party is going to think they're desperate and hold out until they move even further.
Given that market makers are, almost by definition, going to be doing HFT and there will be a market maker as counterparty to any investment trade, the "perfect" market would have 50% HFT matching buyers to sellers.
There is certainly an argument as to whether market makers are really required but, in practice, if they're not there, then I can't see how there can be any more trust in the stock markets than there is trading in ebay.
It's essential that when I buy I know that the stocks will be delivered and when I sell I know that I'll be paid. On ebay I factor in the fact that I might never get the goods into the price that I'm willing to pay.
It has been said that it takes 10,000 hours of practice to get really good at anything.
Even at 10 hours a day this means it will take three years to really learn a language.
I'm trying to learn Turkish - and been at it for about six months now. I'm probably managing to average less than an hour a day of study and it's somewhat depressing to think that it will take 30 years to get anywhere. So I've got Turkish playing in the background most of the time (including now) and I'm pleasantly surprised that I'm now getting pretty good at hearing what is said - to the point where I can often hear words well enough to put them into google translate (not whole sentences yet) and I've even managed to learn a couple of words just from the context of what I'm listening to.
It's not just the geography, it's that English is "everyone's" second language.
So, as an English speaker, unless you just happen to know their first language, your language in common will be English.
I did French at school. I was never very good but I got to the point where I could follow a conversation provided the speakers weren't speaking too fast although I couldn't join in because by the time I'd thought what to say they would be three topics on but since then I've never had a use for French. I've done work in Italy, Germany, Thailand, Dubai but in every case it's been English that has been the language of communication (and in no case did I live in the country so I didn't have a chance to learn a language on the job so to speak)
Had everyone's second language been French then I'm sure I'd be pretty fluent in the language now. Instead it's rusted over the last 20 years to the point that when I am in France I'm struggling to recognise individual words, let alone understand whole sentences.
Gaaaaaaaahhhhhhhhh. I thought this was a website that was supposed to be populated with technical, computer literate people, even programmers.
The end user requirement: "Show the time"
They mean "Show the correct time for my current location"
This is easy: Every (ok, perhaps there's someone still using an old IBM PC computer where you have to set the clock at boot) browser is running on a machine that has a local clock. So we'll use it to display the time.
Some end users then start complaining that the time on the BBC website is wrong.
There's two obvious reasons for this: 1. The user has taken the iphone/ipad whatever on holiday and haven't updated the timezone or 2. Their local clock is just plain wrong.
OK. So we've now established that the end user is incapable of correctly determining and setting the correct time and timezone on their machine. So we, as a programmer, have to do this for them. Cookies, asking the user, etc obviously aren't going to work. If they cannot get their own clock right then they're not going to get the website configuration right either.
This is hard, hard, hard to solve. IMO it's impossible - what do you do about people coming through proxies in different timezones?
The BBC have made exactly the right decision - the old solution was the correct one. PEBKAC. TPTB have decided that the correct solution wasn't good enough. So don't waste any more time or money trying to hack together something just to satisfy end user requirements that are fundamentally broken. End users can use the clock on their machine anyway and they won't complain to the BBC if it's wrong (presumably they complain to Microsoft instead)
It claimed that the product of all the primes up to N and then adding 1 is prime.
The product of all the primes up to 13 is 30031. 2^30030 mod 30031 is 21335 Therefore 30031 is not prime. (Fermat's little theorem)
The proof as stated is insufficient. I have proved that 30031 is not prime but I have not found any prime factors of 30031. Therefore, to complete the proof you need to include the case that 30031 contains a prime factor not in my original list because I have proved that 30031 does not belong in my list.
What I was trying to say is that given a purported complete set of primes, it's impossible to construct a prime not in the list other than by first assuming that there is a prime not in the list.
Any algorithm that tests N+1, N+2... will not terminate if N is the largest prime.
Slashdot Mirror
http://xkcd.com/685/
I cannot directly answer your claim about no studies being published that show smoking is harmless because I haven't read the literature but any reasonably competent researcher could write a paper showing that smoking might be harmless.
The problem with smoking is that the effects happen over a long term and there are many confounding factors to take into account - smokers often have a worse diet for example. At the end of the day the correlation of smoking with harm is the only one that stands up to extended scrutiny but it's not something that can be (easily) proved in a single study.
Bicycle helmet wearing rates are positively correlated with cyclist head injury rates. Countries (and states) that have introduced mandatory helmets have typically seen an increase in head injury rates after the introduction of the law unless the law was not enforced.
But you can find plenty of papers published that suggest that bicycle helmets prevent head injury. I don't know of any that say that bicycle helmet wearing is more dangerous than not (despite the correlation above) although there are also plenty that suggest that there is no net benefit to cycle helmet wearing and there are some that say that the reduction in cycling of mandatory helmet laws have a net deleterious health effect.
Bicycle helmet wearing efficacy testing is hampered by confounding factors. Just as one example, it has been measured that cars pass helmeted cyclists closer than unhelmeted cyclists. My nearest "miss" was being clipped on the arm by the wing mirror of a very fast moving car. I might not be alive today if I'd been wearing a helmet and he'd been two inches closer.
So you cannot just test a helmet in the lab and say that in event A, a helmet is better than no helmet because the frequency of event A might itself depend on the presence or absence of a helmet.
Not only does Mr Cameron not have a peerage but he wouldn't be allowed to sit in the house of commons if he did have a peerage.
Tony Benn had to fight long and hard to renounce his (hereditary) peerage so he could be an MP.
Harla Branno (mayor of Terminus)
Vasilia Aliena (Dr Falstoffs daughter and by all accounts, one of the most brilliant roboticists on Aurora)
Susan Calvin (The Einstein of robotics - still remembered hundreds of years later on a world that considers Earthmen to be little more than monkeys)
Good grief. Have you even read the wikipedia page, let alone the book itself?
From the wiki page:
"The philosophical problem is about the decrease in knowledge when it comes to rare events as these are not visible in past samples and therefore require a strong a priori, or an extrapolating theory; accordingly, predictions of events depend more and more on theories when their probability is small. In the fourth quadrant, knowledge is both uncertain and consequences are large, requiring more robustness."
There has never been as rapid a rise of CO2 as is happening now. The rare event that is happening now is not visible in the geological record.
We started to understand the greenhouse effect way back in the 1850s. By the 1920s we had the knowledge to completely understand it and the data was collected to verify it all by the 1950s.
We've built excellent models for predicting the long term behaviour of the climate due to the CO2 forcings we've introduced. Even the early models from the 1970s predictions have held up to scrutiny and later models are better still. If anything, the various models have tended to underestimate the changes to the climate.
When we extrapolate the current models the potential costs are absolutely catastrophic. In the worst cases it's hard to see how civilization can survive and even human extinction isn't inconceivable. If we'd started mitigating strategies in the 80s it might have cost us a tiny fraction of growth but we chose not to and every year we wait the evidence that we must act gets stronger and the costs higher.
And you're saying that "well we don't completely understand absolutely everything so we should continue running headlong to where the majority of scientists say there is a cliff to fall off" and then you quote a book that says that financial experts tend to underestimate the downsides due to incomplete knowledge as support for your inane views.
I don't know anything at all about German tax law but assuming it's even moderately like the UK then I don't understand why any of this is a surprise.
In the UK you are potentially liable for tax for all gains. Usually it will either be income tax or capital gains tax and as a general rule of thumb, if you buy something at one price with the intention of selling it at a different price it will be CGT while if you "earn" it it will be IT.
Bitcoin mining is an oddity because you don't buy the coins but produce them and I don't know where it falls but I would guess CGT but electricity costs etc would be deductible from any profit before tax was due.
There's an additional 10K allowance per year for CGT and you don't have to report gains below this so most people buying and selling shares for example don't really have to think about it.
Your only or main home is a significant exception where no CGT is payable (nor losses claimable). There are other exceptions - wine, cars.
Also selling things you no longer need is exempt from CGT (again, both for profit and loss) so selling stuff on ebay when you're having a clear out does not involve HMRC but trading (i.e. buying stuff with the intention of selling it again) will do.
On the whole I'd say the UK taxation system is fair and predictable. There are anachronisms - for example, if you jointly own a house with someone who isn't your spouse then any rental income/loss can be apportioned to either party in any proportion (you must let the tax office know the proportion if it doesn't match the ownership proportion) while if you are married then it must be apportioned either 50/50 or in the same proportion as the ownership is shared. Transfers between husband and wife are not reportable for CGT because gains and losses are not crystalized at the point of transfer so the gain is still taxable once the asset is finally disposed of. Capital gains are payable when they are realized - so if you make a 100K gain once in ten years then you will pay tax on 90K in the year you make the gain while if you can crystalize 10K per year you will pay no CGT (i.e. unused CGT allowances cannot be rolled forward) but if you make a big loss in one year then you can roll that forward so that future profits are not taxed until you've made up the loss.
There's a certain amount of effort to harmonize EU tax rules between countries. I would be surprised if the tax laws in Germany were very different - apart from anything else, if they were significantly different I'd have expected to see news reports about people taking advantage of the tax differences between UK and DE.
IANAA (an accountant).
I suspect you're wrong. The average intelligence hasn't really changed much at all.
What has changed is what you're prepared to accept.
When you were 16, the fact that she was pretty and appeared to like you was more than sufficient to keep your interest in her (at least for a while)
Now you're finding that looks aren't nearly enough to keep your interest beyond the first time she opens her mouth.
Give it another ten years and you'll come to realize that looks really don't matter that much at all. You can admire the hot sexy ones from a distance while listening to the intelligent interesting ones. In time you might discover that she's pretty hot and sexy as well as interesting and intelligent - especially if she starts showing more than a social interest in you - and even if you don't you'll have found a new friend.
On the whole I find women more interesting, easier to talk to, and more intelligent than men.
Tim.
This is a very contrived example that I've hacked together to show the possibly unanticipated problems of using auto and, in particular, changing code that has types explicitly coded to use auto instead:
$ g++ -std=c++0x -o auto auto.cpp ./auto
$
I am a PublicClass with value 10
I am a PrivateClass with values 4 and 6
$
char c = 4;
What is the type and value of the following expression?
c + 2
While I like the new auto syntax I'm a little scared about having to deduce what the type is when incompetent programmers start using auto because they don't know what the correct type should be.
Much like my heart sinks when I see code using void* to store and pass pointers around and then cast them when they arrive at their destination.
In one codebase (a few tens of thousands of lines) I was tasked with addressing all the intermittent and unreproducible problems. More than 90% of the bugs were revealed just by replacing the void* with a pointer to the type that was actually being held, removing the casts, and then fixing whatever the compiler barfed on when there were incompatible types.
Tim.
Amen!
Something similar happens at the BBC Proms whenever there's a piano concerto.
The leader of the orchestra plays an A and then the prommers at the front applaud (This is just the done thing, like shouting "Heave" when the lid of the piano is opened - to which the gallery reply "Ho".) Sometimes the leader takes a bow, sometimes they just ignore it.
But sometimes the applause grows to the point where half the hall is clapping (but not the prommers who started it all)
Tim.
Reminds me of that Oscar Wilde joke.
Wilde comes down to lunch.
"Written another chapter of your book Oscar?"
"No. I spent this morning putting in a comma"
Wilde comes down to dinner.
Sarcastically, "Put another comma into your book Oscar?"
"No! I took out the comma I put in this morning."
You are right that in theory you can be a market maker without clearing but true market makers are members of the exchange. Being a market maker gives them certain extra freedoms and certain extra obligations.
And being a member of the exchange means that you get clearing.
It's not easy to predict what might happen if there wasn't true market makers.
Tim.
No. This isn't how it works.
Johnny wants to buy an apple at up to 49p. Chris wants to sell an apple at no less than 52p.
They're both sitting there doing nothing.
Flash the wonder trader decides that Johnny and Chris are both prepared to negotiate by up to 2p on what they say is their best offer.
So Flash the wonder trader puts in a bid of 50p and an ask of 51p. This, because it's a better offer, sits ahead of both Chris's and Johnny's trades. Johnny decides that while Chris's 52p wasn't good enough, he'll take Flash's 51p offer to sell and Chris decides that while Johnny's 49p wasn't good enough, Flash's 50p offer to buy is good enough.
Flash pockets the 1p and he's happy.
Note that Flash can actually make the market work - Both Johnny and Chris are sitting there unwilling to make the first move towards a compromise - each is thinking that if they move first then the other party is going to think they're desperate and hold out until they move even further.
Tim.
60% being HFT doesn't sound unreasonable to me.
Given that market makers are, almost by definition, going to be doing HFT and there will be a market maker as counterparty to any investment trade, the "perfect" market would have 50% HFT matching buyers to sellers.
There is certainly an argument as to whether market makers are really required but, in practice, if they're not there, then I can't see how there can be any more trust in the stock markets than there is trading in ebay.
It's essential that when I buy I know that the stocks will be delivered and when I sell I know that I'll be paid. On ebay I factor in the fact that I might never get the goods into the price that I'm willing to pay.
Tim.
It has been said that it takes 10,000 hours of practice to get really good at anything.
Even at 10 hours a day this means it will take three years to really learn a language.
I'm trying to learn Turkish - and been at it for about six months now. I'm probably managing to average less than an hour a day of study and it's somewhat depressing to think that it will take 30 years to get anywhere. So I've got Turkish playing in the background most of the time (including now) and I'm pleasantly surprised that I'm now getting pretty good at hearing what is said - to the point where I can often hear words well enough to put them into google translate (not whole sentences yet) and I've even managed to learn a couple of words just from the context of what I'm listening to.
Tim.
It's not just the geography, it's that English is "everyone's" second language.
So, as an English speaker, unless you just happen to know their first language, your language in common will be English.
I did French at school. I was never very good but I got to the point where I could follow a conversation provided the speakers weren't speaking too fast although I couldn't join in because by the time I'd thought what to say they would be three topics on but since then I've never had a use for French. I've done work in Italy, Germany, Thailand, Dubai but in every case it's been English that has been the language of communication (and in no case did I live in the country so I didn't have a chance to learn a language on the job so to speak)
Had everyone's second language been French then I'm sure I'd be pretty fluent in the language now. Instead it's rusted over the last 20 years to the point that when I am in France I'm struggling to recognise individual words, let alone understand whole sentences.
Tim.
Vicious, Independent, Replicating, Unswerving, Sacrificial robots.
I think we need a special word for them...
hmmm .... VIRUS robots
The time at the BBC is an institution.
http://en.wikipedia.org/wiki/Greenwich_Time_Signal
The right to read out the time on the Today programme has been auctioned for charity.
People in the UK expect the time from the BBC to be right.
Unfortunately, the internet has meant that there are now variables that the BBC cannot control for.
Tim.
Gaaaaaaaahhhhhhhhh. I thought this was a website that was supposed to be populated with technical, computer literate people, even programmers.
The end user requirement: "Show the time"
They mean "Show the correct time for my current location"
This is easy: Every (ok, perhaps there's someone still using an old IBM PC computer where you have to set the clock at boot) browser is running on a machine that has a local clock. So we'll use it to display the time.
Some end users then start complaining that the time on the BBC website is wrong.
There's two obvious reasons for this: 1. The user has taken the iphone/ipad whatever on holiday and haven't updated the timezone or 2. Their local clock is just plain wrong.
OK. So we've now established that the end user is incapable of correctly determining and setting the correct time and timezone on their machine. So we, as a programmer, have to do this for them. Cookies, asking the user, etc obviously aren't going to work. If they cannot get their own clock right then they're not going to get the website configuration right either.
This is hard, hard, hard to solve. IMO it's impossible - what do you do about people coming through proxies in different timezones?
The BBC have made exactly the right decision - the old solution was the correct one. PEBKAC. TPTB have decided that the correct solution wasn't good enough. So don't waste any more time or money trying to hack together something just to satisfy end user requirements that are fundamentally broken. End users can use the clock on their machine anyway and they won't complain to the BBC if it's wrong (presumably they complain to Microsoft instead)
Tim.
Gah. ... so X+1 is probably prime.
I did. I've also now tested it more fully and I think it's wrong.
The product of the first 75 primes (up to 379) is X=1719 620105 458406 433483 340568 317543 019584 575635 895742 560438 771105 058321 655238 562613 083979 651479 555788 009994 557822 024565 226932 906295 208262 756822 275663 694110
2^X mod X+1 is 1 so X+1 is probably not prime.
Tim.
No!
The original proof is flat out wrong.
It claimed that the product of all the primes up to N and then adding 1 is prime.
The product of all the primes up to 13 is 30031.
2^30030 mod 30031 is 21335
Therefore 30031 is not prime. (Fermat's little theorem)
The proof as stated is insufficient. I have proved that 30031 is not prime but I have not found any prime factors of 30031. Therefore, to complete the proof you need to include the case that 30031 contains a prime factor not in my original list because I have proved that 30031 does not belong in my list.
Tim.
http://www.math.psu.edu/sellersj/courses/math035/fa11/handouts/07_infinitely_many_primes.pdf
1) This proof is not a âoeconstructiveâ proof. We do not build an infinite list of primes in the process. This is a proof by contradiction.
Yes, Sorry. My comment wasn't very well written.
What I was trying to say is that given a purported complete set of primes, it's impossible to construct a prime not in the list other than by first assuming that there is a prime not in the list.
Any algorithm that tests N+1, N+2... will not terminate if N is the largest prime.
Tim.