--- In

primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:

>

> --- In primenumbers@yahoogroups.com,

> "Mark Underwood" <mark.underwood@> wrote:

>

> > Here's a hint: (n-1) is a factor of (n^n-n).

>

> The stakes have risen, Mark.

>

> You have to explain 3 features of the data that

> Richard Heylen has exposed:

>

> 1) some primes stay as divisors at successive higher powerings;

> 2) some disappear for ever after a single division;

> 3) some pop in, pop out, then pob back, then stay put.

>

> To how many of those features of the data does your

> gnomic "hint" apply? If not to all 3, then why not?

>

> Thanks, in any case, for your interest

>

> David

>

Feature number one, where some primes stay forever as divisors, is a natural consequence. Specifically, if a factor appears twice in a row at two successive powerings, it will remain from then on. Why some prime divisors appear only once while others flit in and out and others never make an appearance, those are details that could be worked out I'm sure.

Mark