r3769
Posts:
30
Registered:
12/12/04


Are these numbers always prime?
Posted:
Nov 19, 2000 4:21 PM


Suppose n and b are positive integers. Set x[0]=(n1)/n and recursively compute:
x[i+1]=x[i]*ceil(b*x[i])b
until x[i+1]=0.
Now set l(b,n)=i+1. For example, l(2291,11)=10.
Empirical evidence suggests: if l(b0,n)=n1 then there exists a c0 s.t. l(b0+c0*k,n)=n1 for k>0.
Examples: l(423953,17)=16, c0=720720 l(2579419,19)=18, c0=17*720720 l(30364247,23)=22, c0=19*17*720720
Consider the set Q={n:l(b,n)=n1 for some b}. Are these numbers always prime?
Rich Burge

