Prime-generating fractions(johndcook.com)

86 pointsby lesterbuck13 anni fa8 comments

http://www.johndcook.com/blog/2013/10/12/prime-generating-fractions/

5 comments

The 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)

svnfv13 anni fa

This 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.

juliajuli4513 anni fa

pontifier13 anni fa

so, 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.

Someone13 anni fa

No. 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... or http://www.math.sunysb.edu/~tony/whatsnew/column/irrational-...

abecedarius13 anni fa

From the title I expected http://en.wikipedia.org/wiki/FRACTRAN (see the list of fractions at the top).

mathattack13 anni fa

It borrows one problem from Project Euler and seems to scream for another.

yeukhon13 anni fa

Okay. 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?

inglesp13 anni fa

I 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.

KatherineJMoses13 anni fa