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Prime-generating fractions
- pontifier 13y agoThe way this is constructed is interesting, but it doesn't appear that a real sequence to generate primes is required, just a list of them: D=0 SUM=0 for n: D += num_digits(PRIME[N]) // +1 for a nice single 0 between them SUM += PRIME[n]/(10^D) print fraction(SUM)
- pontifier 13y agoso, you could even skip the math and just append the string representations of the primes. It seems the really difficult part is finding a good simple fraction to express the string. Perhaps that's the key here. maybe the primes summed in the sequences are a subset that produces a relatively simple fractional representation.
- Someone 13y agoNo. If you know some theorems about continued fractions, finding such rational numbers is easy. Just generate best rational approximations until you have one that is close enough. See for example http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#real http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci... or http://www.math.sunysb.edu/~tony/whatsnew/column/irrational-0799/irrational3.html http://www.math.sunysb.edu/~tony/whatsnew/column/irrational-...
- svnfv 13y agoThis method results in much shorter numerators and denominators than the list of primes it generates. Simplifying this fraction only chops off 2 or so digits on average.
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- mathattack 13y agoIt borrows one problem from Project Euler and seems to scream for another.
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- yeukhon 13y agoOkay. Very interesting. For those who don't understand like me, what is the technical use of this? Where will this be used? Are we somehow going to use this in cryptography?
- inglesp 13y agoI don't think it does have a technical use. You certainly couldn't use this technique to generate new primes, since the fractions have been deliberately chosen based on the primes they will generate. As it stands, it's just a fun mathematical curiosity.
- abecedarius 13y agoFrom the title I expected http://en.wikipedia.org/wiki/FRACTRAN http://en.wikipedia.org/wiki/FRACTRAN (see the list of fractions at the top).