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Topic: Are these numbers always prime?
Replies: 3   Last Post: Nov 21, 2000 5:33 PM

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r3769

Posts: 30
Registered: 12/12/04
Are these numbers always prime?
Posted: Nov 19, 2000 4:21 PM
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Suppose n and b are positive integers. Set x[0]=(n-1)/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)=n-1 then there exists a c0 s.t.
l(b0+c0*k,n)=n-1 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)=n-1 for some b}. Are these numbers always
prime?

Rich Burge








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