## 20523Re: Small prime divisors of very large numbers

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• Jun 30, 2009
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"Jens Kruse Andersen" <jens.k.a@...> wrote:

> > The first 7 primes that divide
> > 137^(137^(137^(137^137))) + 73
> > are 2, 3, 5, 29, 821, 23339, 67525153.
> >
> > Puzzle: Find the first 7 primes that divide
> > 137^(137^(137^(137^(137^137)))) + 73
>
> The same.

As might have been expected, Jens was the first
to post what I believe to be the correct solution.

Almost at the same time, Richard FitzHugh
sent me, privately, the same answer:

> I get the same first 7 primes to divide your larger number
> (namely 2, 3, 5, 29, 821, 23339, 67525153). This seems very
> strange indeed! It took about 6 minutes of actual processor
> time, after about 20 minutes of trying to accurately place
> all the brackets in the nested eulerphi calls!

Like Richard, I find this result to be "strange indeed".

Can anyone tell Richard and me why we should not be surprised?

With thanks to all concerned

David
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