## 10647RE: [PrimeNumbers] Re: Is phi(p^2-1)/(p^2-1) bounded?

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• Jan 4, 2003
--- Jon Perry <perry@...> wrote:
> 'm=1;mp=430*10^6; \\ Jon please note
> forprime(p=2,mp,n=p^2-1;s=eulerphi(n)/n;if(s<m,m=s;print(p)))'
>
> I'm looking...
>
> 'Use 'calc' instead. Or bc. Or the other 'calc'. Or use gp and use
> 'p=nextprime(p+1)' rather than 'forprime(p='.'
>
> Is this the K.R. Matthews Number Theory calculator 'calc'?

Possibly. I'm using Chongo's calc (Curt Landon Noll, record prime finder 2-3
decades ago), which is the standard 'GNU' utility. The whereabouts of the
other calc is answered in the archives some time around a year back, maybe
more.

> Is there such a concept as the 'average value of f(p)'?

I expect it to drift downards so it's not well-defined.
(or maybe it is, maybe it's zero. On average numbers have 1/eps distinct
divisors, i.e. a divergent number. That's got to take a toll on the phi
value. Any sample up to 300000# is puny compared with the sizes of almost
all integers...)

Phil

=====
The answer to life's mystery is simple and direct:
Sex and death. -- Ian 'Lemmy' Kilminster

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