It took me a few minutes to get this too. It relies on the fact that the sum of the digits of a number is congruent to the number itself mod 3 (which is easy by induction).
This proof covers both parts of the original assertion, i.e. n = 0 mod 3 implies both that nth and (n-1)th terms of sequence are equal to 0 mod 3.
The assertion is clearly true for n=3.
Now for the case where you're adding n on at the end. This number looks like:
{the (n-3)rd number in the sequence}{digits of n-2}{digits of n-1}{digits of n}
The n-3rd number is divisible by 3 by the induction hypothesis. The digits of n-2 and n-1 are respectively -2 and -1 mod 3, so adding them together is 0 mod 3, and n itself is 0 mod 3, so the nth term of the sequence must also be divisible by 3.
Getting het up means getting annoyed or irritated. So the phrase becomes : Me getting annoyed about their poor grammar seems likely to make me one of them.
Alternative version : If I get annoyed about their poor grammar, I am likely to become one of them.
Bad form to reply to myself, sorry, but another way to think of it is to look at the differences between consecutive primes.
Say d(n) = p(n+1) - p(n).
Write down d(n) as a list of numbers.
It'll bounce around all the time (see other posts for proof that you can always find a value as large as you like), but you'll also always be able to find a value that's 600 or less, and at that point you've found a "nearby pair."
The holy grail of the full twin prime conjecture is just saying that there are an infinite number of 2s in the sequence of d(n)s.
There exists an infinite sequence of primes p_n for which there is another prime somewhere in the range between p_n + 2 and p_n + 600.
It isn't trying to cover every prime, just saying that no matter how far you go along them, you'll always be able to find another "nearby pair" further on.
The holy grail of the exercise is to bring the 600 down to 2, so that we'll be able to say there are an infinite number of so-called twin primes.
Given sensitive enough instruments or a large enough "spaceship", you can tell the difference, because of the inverse square law.
Anything massive enough to generate 1g of gravitational force will generate a different field strength over the volume of the spaceship - the acceleration would be slightly lower than 1g at the point furthest from the centre of mass, and higher than 1g at the point closest to the centre of mass. A spaceship of width 20m orbiting the earth at 500 km height, say, would only have about a 1 in 10000 difference between nearest and furthest, though.
If you're accelerating using a rocket drive, the acceleration would be uniform over the whole volume of the ship. That's assuming, of course, the rocket's acceleration could be kept at exactly 1g, which, again, depends on how sensitive your instruments are.
Someone else has already explained "the Open era", so I'll just add my bit to say that Wimbledon is also known as the British Open, in the same way as the French Open is often referred to as Roland Garros.
The EU settlement is, AFAIK, a cash sum.
Since the likely outcome for this case will be for that $1.5bn to be in the form of Windows discount vouchers, I wouldn't think they'll be too bothered.
I first noticed it in the first ep of season 6. Spike saves Giles from a vampire, and Giles thanks him and says "My whole life flashed before my eyes."
Spike replies with something like "Must have been fun. Cup of tea, cup of tea, almost got shagged... cup of tea."
The BBC completely ruined the joke by cutting out "almost got shagged!"
There's a cap on the cost of the claim in any individual company's case - the company chooses how much cover it wants (see article - you get $25m of cover for $1m premium, and there's probably also a limit to x% of the company's annual profits).
The insurance company will itself be insured against very big losses from a single event (although that's really just passing some of the buck, to mangle a metaphor, as SOMEONE's got to pay eventually - several reinsurance companies posted huge losses due to 11th September claims).
I would expect that there would be some clause to limit the amount of a claim in the event of a domino effect like this, in the same way as "regular" policies don't cover nuclear war - which is what something like this would amount to in terms of effect on the Net.
I'm an actuary by training, and we call this issue "moral hazard".
One of the best ways to reduce the risk to the insurance company is to introduce "self-insurance" where the customer has claim to bear some of the cost of any claim - like the excess on your car insurance policy. For these policies, the customer's probably liable for something like the first $5 or $10 million of any claim.
I'd also expect the insurance company to follow up any large claims with another audit, to see if any of the security controls and procedures had become lax since the time the policy was taken out, and there'll be a standard clause to reduce/invalidate the claim if anything's found in this audit.
David Palmer's second book was called "Threshold" - I think it was meant to be part of a trilogy, but I heard he'd died, rather than retired.
"Emergence" is probably my favourite SF book of all time , and is even more amazing for being his first novel - sadly out of print now (at least here in the UK. Threshold's good, but not a patch on his first.
Slashdot Mirror
This proof covers both parts of the original assertion, i.e. n = 0 mod 3 implies both that nth and (n-1)th terms of sequence are equal to 0 mod 3.
The assertion is clearly true for n=3.
Now for the case where you're adding n on at the end. This number looks like:
{the (n-3)rd number in the sequence}{digits of n-2}{digits of n-1}{digits of n}
The n-3rd number is divisible by 3 by the induction hypothesis. The digits of n-2 and n-1 are respectively -2 and -1 mod 3, so adding them together is 0 mod 3, and n itself is 0 mod 3, so the nth term of the sequence must also be divisible by 3.
Alternative version : If I get annoyed about their poor grammar, I am likely to become one of them.
Say d(n) = p(n+1) - p(n).
Write down d(n) as a list of numbers.
It'll bounce around all the time (see other posts for proof that you can always find a value as large as you like), but you'll also always be able to find a value that's 600 or less, and at that point you've found a "nearby pair."
The holy grail of the full twin prime conjecture is just saying that there are an infinite number of 2s in the sequence of d(n)s.
It isn't trying to cover every prime, just saying that no matter how far you go along them, you'll always be able to find another "nearby pair" further on.
The holy grail of the exercise is to bring the 600 down to 2, so that we'll be able to say there are an infinite number of so-called twin primes.
The speed of light is faster in uranium than in water? Really?
Anything massive enough to generate 1g of gravitational force will generate a different field strength over the volume of the spaceship - the acceleration would be slightly lower than 1g at the point furthest from the centre of mass, and higher than 1g at the point closest to the centre of mass. A spaceship of width 20m orbiting the earth at 500 km height, say, would only have about a 1 in 10000 difference between nearest and furthest, though.
If you're accelerating using a rocket drive, the acceleration would be uniform over the whole volume of the ship. That's assuming, of course, the rocket's acceleration could be kept at exactly 1g, which, again, depends on how sensitive your instruments are.
Someone else has already explained "the Open era", so I'll just add my bit to say that Wimbledon is also known as the British Open, in the same way as the French Open is often referred to as Roland Garros.
The EU settlement is, AFAIK, a cash sum. Since the likely outcome for this case will be for that $1.5bn to be in the form of Windows discount vouchers, I wouldn't think they'll be too bothered.
Gnu's Not Anything, Actually?
I first noticed it in the first ep of season 6. ... cup of tea."
Spike saves Giles from a vampire, and Giles thanks him and says "My whole life flashed before my eyes."
Spike replies with something like "Must have been fun. Cup of tea, cup of tea, almost got shagged
The BBC completely ruined the joke by cutting out "almost got shagged!"
that the claim's only for $10 million or so, but these are particularly fast dollars.
But not as fast as Clear Channel claim they'll be!
The insurance company will itself be insured against very big losses from a single event (although that's really just passing some of the buck, to mangle a metaphor, as SOMEONE's got to pay eventually - several reinsurance companies posted huge losses due to 11th September claims).
I would expect that there would be some clause to limit the amount of a claim in the event of a domino effect like this, in the same way as "regular" policies don't cover nuclear war - which is what something like this would amount to in terms of effect on the Net.
One of the best ways to reduce the risk to the insurance company is to introduce "self-insurance" where the customer has claim to bear some of the cost of any claim - like the excess on your car insurance policy. For these policies, the customer's probably liable for something like the first $5 or $10 million of any claim.
I'd also expect the insurance company to follow up any large claims with another audit, to see if any of the security controls and procedures had become lax since the time the policy was taken out, and there'll be a standard clause to reduce/invalidate the claim if anything's found in this audit.
And in Soviet Russia, it'll be the other way around...
David Palmer's second book was called "Threshold" - I think it was meant to be part of a trilogy, but I heard he'd died, rather than retired. "Emergence" is probably my favourite SF book of all time , and is even more amazing for being his first novel - sadly out of print now (at least here in the UK. Threshold's good, but not a patch on his first.