Phil:

> That's a completely sideways way of looking at things!

> I like it!

Thank ye, kind sir.

> I think one of my results was a {1,4,6} wasn't it?

Yep. I said you didn't need to bother, not that you

didn't bother.

> I'm surprised it works, because the factors need to

> be of a particular residue in order to make the thing

> carmichael

\begin{explanation}

lcm{1,2,12}=3*4

We get the 3 from 4*x+3, since

x=0 mod 3, because of the primorial.

We get the 4 from (1+1/d).

All possible d's are odd.

So half of the combinations of ECM primes work.

But we double these using the 5 from 6*x+5,

since x=0 mod 5, because of the primorial.

So {1,2,12} is as rich as {1,2,3}.

Except that it's twice as fast

as {1,2,3} for ECMing.

\end{explanation}