3 Jun
2013
3 Jun
'13
11:23 p.m.
On 6/4/2013 1:05 AM, Dan Asimov wrote:
What if any is the current thinking on this question:
Does there exist any nontrivial integer polynomial
f(x) := A_n x^n + . . . + A_0
with n > 0 and A_n > 0, such that for some positive integer K the sequence
K, f(K), f(f(K)), f(f(f(K))), . . .
contains infinitely many primes?
What do you mean by "nontrivial"? f(x) = x + b will work for any positive b and any K coprime to b (by Dirichlet's theorem). If f(x) = 2x + 1 and K = 1, then the resulting sequence contains the Mersenne numbers. It is widely believed that there are infinitely many Mersenne primes. -- Fred W. Helenius fredh@ix.netcom.com