On 10-10-14 1:15 PM, Rich Cooper wrote:
Hi Doug,
Thanks for you post, you seem to
be honestly trying to understand 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. But I
expected Menzel to make an honest answer instead of an ad
hominem attack.
The point is that there is no
function which takes primes as its domain
and ranges over the primes.
Actually, there is indeed such a function.
Matiyasevich's theorem says:
- Every recursively enumerable set is Diophantine,
that is, every recursively enumerable set is equivalent to the
integer solutions of some polynomial.
Since the set of prime numbers is recursively enumerable, there
exists a polynomial function
whose integer solutions are exactly the prime numbers.
You might even check out the page
http://en.wikipedia.org/wiki/Prime_number_formulas
for examples of such functions.
As a wise person said earlier in this thread
"we've made progress if you get off the soap box. "
- michael