--- In primenumbers@yahoogroups.com,
"Mike Oakes" <mikeoakes2@...> wrote:

> David, I agree completely that your observation that the
> Fermat-Euler theorem [Hardy & Wright, Theorem 72] failing
> if gcd(x,m) <> 1 is the core of all the problems

In the middle of working on something quite different I had
an odd feeling of H&W frowning at me from the bookshelf.

I chose base 137 hoping to miss the gcd problem,
but it's notable that the pop-in, pop-out, pop-in prime
3686183, in Richard Heylen's message
http://tech.groups.yahoo.com/group/primenumbers/message/20545
is one for which one needs to be more careful:

x=3686183;
for(k=1,10,x=eulerphi(x);print(if(x%137,x,whoops)))

3686182
1843090
737232
245728
whoops
34816
16384
8192
4096
2048

Tricky stuff, not so?

David