Re: loose ends

From: George Murphy (gmurphy@raex.com)
Date: Sun Aug 03 2003 - 16:32:34 EDT

  • Next message: Glenn Morton: "RE: loose ends"

    Glenn Morton wrote:
    >
    > Hi George, I include a note to Burgy at the bottom.
    >
    > >-----Original Message-----
    > >From: George Murphy [mailto:gmurphy@raex.com]
    > >Sent: Sunday, August 03, 2003 1:04 PM
    > >To: Glenn Morton
    > >Cc: asa@calvin.edu
    >
    > George originally wrote:
    >
    > >> > There is a basic difference between the Fibonacci sequence
    > >> >& the primes. As you
    > >> >note, there is a formula with which one can generate as many
    > >> >members of the 1st sequence
    > >> >as you wish. But there is no general formula for generating
    > >> >primes (unless there's been
    > >> >a new discovery I haven't heard of, a possibility since I'm hardly
    > >> >a number theorist).
    > >> >All proposed prime-generating formulas have been found to break
    > >> >down at some point.
    >
    > After my mention of the sieve of Eratosthenes he writes:
    >
    > > Don't need to - I learned about it from Gamow's _One, Two,
    > >Three ... Infinity_
    > >when I was about 14. It isn't a prime-generating formula but a device for
    > >systematically checking to see if numbers are prime. By a
    > >proposed prime-generating
    > >formula I mean something like
    > > f(n) = n^2 - n + 41
    > >which gives primes for n = 1, 2, ... 40 but for n = 41 gives a
    > >perfect square.
    >
    > Ok, there isn't such a simple formula but why does a simple formula mean
    > anything? There is a prescription for how to iteratively catch the primes
    > and another but simpler formula for catching the numbers in Fibonacci. I
    > don't see what 'simple' has to do with it.

    Glenn -
            Simplicity isn't the issue. There isn't even a complicated formula or
    prescription for generating primes. The formula for the Bernoulli numbers, e.g., is a
    good deal more involved than that for the Fibonacci sequence
    (Bn = (2n)!Z(2n)/2^(2n-1)*pi^2n, where Z is the zeta function) but it's a formula into
    which you (or a computer) can plug n = 1,2, 3 .. and generate as many as you wish.
    The sieve doesn't work that way. What you're doing with it is seeing if n is prime by
    checking multiples of all the integers up to n-1 & if none of them is n then n is prime.

                                                            Shalom,
                                                            George

    George L. Murphy
    gmurphy@raex.com
    http://web.raex.com/~gmurphy/

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