"I came here in a taxi with the number 1729.
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"I came here in a taxi with the number 1729. What a dull number that is."
"On the contrary, it's a very interesting number! When it appears on my clock, it means it's one minute to going-home time."
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"I came here in a taxi with the number 1729. What a dull number that is."
"On the contrary, it's a very interesting number! When it appears on my clock, it means it's one minute to going-home time."
@simontatham wasn't there some quote about it being some Ramanujan number or smth? I remember the first part from somewhere. Maybe not the same number but could be. (Ah yeah wikipedia says it is. Must be true then.
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"I came here in a taxi with the number 1729. What a dull number that is."
"On the contrary, it's a very interesting number! When it appears on my clock, it means it's one minute to going-home time."
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@simontatham wasn't there some quote about it being some Ramanujan number or smth? I remember the first part from somewhere. Maybe not the same number but could be. (Ah yeah wikipedia says it is. Must be true then.
)@cobratbq yes – that's the original version which I'm spoofing.
Hardy went to see Ramanujan and remarked that his taxi had had that dull number. Ramanujan knew it wasn't dull, because it's 10³ + 9³ and also 12³ + 1³, and no smaller integer can be written as two different sums of cubes like that.
(I presume he knew that because he'd once noticed that 12³=1728 and 9³=729 ended in nearly the same digits, and followed up to see if there was an interesting consequence of that.)
That story was enough to make 1729 a very famous integer among mathematicians. But it later turned out to have a _second_ interesting property! It's also a Carmichael number, which are numbers that look enough like primes to consistently fool the otherwise-pretty-good Fermat primality test, even though they aren't prime at all.
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@cobratbq yes – that's the original version which I'm spoofing.
Hardy went to see Ramanujan and remarked that his taxi had had that dull number. Ramanujan knew it wasn't dull, because it's 10³ + 9³ and also 12³ + 1³, and no smaller integer can be written as two different sums of cubes like that.
(I presume he knew that because he'd once noticed that 12³=1728 and 9³=729 ended in nearly the same digits, and followed up to see if there was an interesting consequence of that.)
That story was enough to make 1729 a very famous integer among mathematicians. But it later turned out to have a _second_ interesting property! It's also a Carmichael number, which are numbers that look enough like primes to consistently fool the otherwise-pretty-good Fermat primality test, even though they aren't prime at all.
@simontatham i don't think I knew the part about Carmichael number.
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@simontatham i don't think I knew the part about Carmichael number.
@cobratbq no, I think people who tell the Ramanujan story don't normally go on to mention that connection.
People who teach about Carmichael numbers totally do, though!
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