Loading ...
Sorry, an error occurred while loading the content.

24978Re: [PrimeNumbers] What if Mr. X would have a formula for the prime series?

Expand Messages
  • Jack Brennen
    Apr 2, 2013
    • 0 Attachment
      That formula should read:

      x + (sum for n=x to Infinity of floor(1/F(n!,x!)))


      On 4/2/2013 4:54 PM, Jack Brennen wrote:
      > There are computationally inefficient formulas:
      >
      > Define a function F(a,b) to be equal to a/gcd(a,b^10).
      >
      > Next_prime(x) is then equal to:
      >
      > sum for n=x to Infinity of floor(1/F(n!,x!))
      >
      > I believe this function is correct for all integers x >= 0.
      >
      > In practice, you only need to sum until you get a zero value,
      > and all subsequent values will be zero.
      >
      > What makes the above computationally infeasible, even for relatively
      > small numbers, is that x! is already beyond representation in any
      > known computer long before finding primes becomes difficult.
      >
      >
      >
      >
      > On 4/2/2013 12:43 PM, whygee@... wrote:
      >> Le 2013-04-02 21:34, viva8698 a écrit :
      >>> Recently we had a great discussion during a meeting with colleague
      >>> matematicians and we opened a theme that seems to get quite an
      >>> interesting intellectual quiz:
      >>>
      >>> What would be the consequences if Mr. X would have a formula to
      >>> calculate from a given prime the whole ordered series of the
      >>> subsequent primes one after the other?
      >>
      >> There is no such computationally efficient *formula*.
      >>
      >> However there are _algorithms_, with obvious drawbacks.
      >> It's not what most mathematicians want, hope or dream of,
      >> but Mathematics is not created to please us either.
      >>
      >>
      >> ------------------------------------
      >>
      >> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      >> The Prime Pages : http://primes.utm.edu/
      >>
      >> Yahoo! Groups Links
      >>
      >>
      >>
      >>
      >>
      >>
      >
      >
      >
      > ------------------------------------
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      > The Prime Pages : http://primes.utm.edu/
      >
      > Yahoo! Groups Links
      >
      >
      >
      >
      >
    • Show all 16 messages in this topic