On Thursday October 14 2010, John F. Sowa wrote:
> On 10/14/2010 1:15 PM, Rich Cooper wrote:
> > what I meant by the statement "there is no function that can
> > iterate the primes", and perhaps I should have originally said
> > "directly, without iterating other types", which seems to have set
> > off this mess.
>
> The word 'iterate' seems to be the trigger that created the mess.
>
> I would interpret your wish in the following terms:
>
> Find a closed-form expression that defines a function Pr(n), which
> for any positive integer n produces the n-th prime.
>
> In other words, you want a statement of the following form that
> computes the n-th prime:
>
> Pr(n) = some algebraic expression that uses n, but does not
> contain any nested or implied loop or recursive function. (01)
By that definition, adding one to an integer would not qualify as
iteration, since there is an iterative process of propagating carries
from one bit to the next of the binary representation used by every
digital computer in use. (02)
I still maintain your definition of iteration as distinct from other
recursive functions is specious. (03)
> I agree that no such definition exists.
>
> John (04)
Randall Schulz (05)
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