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very neat. it's bothered me just how many GWh we've collectively poured into bitcoins. is this of any practical use (cryptography?), or is it for pure mathemat
by brey 12y ago
very neat. it's bothered me just how many GWh we've collectively poured into bitcoins.
is this of any practical use (cryptography?), or is it for pure mathematical interest?
(not saying the latter is inferior ...)
- tacotime 12y agoI think the answer might be that for now it's mathematical interest but no one really knows what it might or might not turn into. I think the more of these sextuplet, twin etc. primes that we discover the closer it may be bringing us to developing a grand theory of primes and solving difficult problems like the twin prime conjecture and whatever else is out there. And if we could do that then that would be where the practical ramifications would start to possibly emerge. So for now I see it as just more data that might or might not help spark something in the mind(s) of some mathematical genius(es) one day. I am in no way an expert and this is just amateur speculation but I wanted to write it anyways because I was (am) wondering the same thing.
- xamuel 12y agoMathematician here, have to disagree. Knowledge about individual primes (or n-tuples) is pretty much useless for understanding the big picture of them. And if things like "solving the twin prime conjecture" had practical applications, we wouldn't need to solve them to reap them: if there's a crypto-technique that hinges on TPC being true, you can start using it today, and if it somehow breaks, congratulations, you disproved the conjecture.
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- wbhart 12y agoI absolutely agree with that. But there can be exceptions. For example the ternary Goldbach conjecture boiled down in the end (after a lot of analytic "pencil sharpening" as the author called it) to an exhaustive computer search up to some limit. Of course that was an exceptional case. There were some very committed computational people who had been working on related stuff for years prior who just happened to have the code that could just about reach the required limit with sufficient hardware, which we just happened to have sitting around in between working on projects paid for by our grant. By the time the real theoretical work was done with pencil and paper, the computational task was just completing, meaning the result could be stated unconditionally. Whether you would say that the computer search allowed us to learn anything mathematically useful, though is a state of mind. Mathematicians care much more about techniques than knowing large lists of otherwise random looking numbers, even if conjectures about such lists do motivate looking for new techniques, and even if there is some prestige in having established a long-lived conjecture.
- Someone 12y agoI would say that, for now, the statement *"any odd integer > 5 can be written as the sum of three primes"* is at best a tiny bit better than the N"any odd integer > exp(3100) can be written as the sum of three primes" that we had before or even than the even weaker *"any sufficiently large odd integer can be written as the sum of three primes"* That would change (for me) if we ever link that magical constant 5 to another magic constant 5 in math, or if we create a series of related constants (sums of 4 primes? Sums of three numbers of the form pq with p and q prime? Who knows?) and show a pattern in them. That, I think, is another good reason to try and pinpoint the exact values of these limits. The values the,self are dull, but knowing them may give mathematicians ideas about why they have the values they have. It may often be (relatively) dumb work, but still worth doing.
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- mkramlich 12y agowait til you learn how many GWh we've put into USD, euros, coins, paper currency, banks, accountants, taxes, paperwork, ATM's, etc etc etc :-)