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Prime-generating fractions

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Re: Prime-generating fractions

#2

Post by pontifier »

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)

Re: Prime-generating fractions

#4

Post by pontifier »

pontifier wrote: post #2

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)

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.

Re: Prime-generating fractions

#5

Post by KatherineJMoses »

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Re: Prime-generating fractions

#6

Post by svnfv »

pontifier wrote: post #2

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)

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.

Re: Prime-generating fractions

#7

Post by juliajuli45 »

svnfv wrote: post #6
pontifier wrote: post #2

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)

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.

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Re: Prime-generating fractions

#8

Post by Someone »

pontifier wrote: post #4
pontifier wrote: post #2

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)

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.

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-...

Re: Prime-generating fractions

#10

Post by inglesp »

yeukhon wrote: post #9

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?

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.

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