--- In

primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> 1) My code is modelled on Bill's and hence is very inefficient.

> It is notable that Bill requires 55 Lucas tests to conclude

> that 1412759 is probably prime

> 2) It is easy to find larger pseudoprimes.

> Here are 5 greater than 2*10^9:

> fooled=[2023351681,2050864921,2099611801,2189197501,2201924341]

> 4) Finally, the promised Pinch, using,

> http://www.chalcedon.demon.co.uk/rgep/p20.pdf

> which reveals that Bill's algorithm cannot decide on the

> status of N = 443372888629441, even if we allow him

> to spend 200,000 selfridges

Ah, I see that I forgot the third coffin-nail. Here it is:

3) If Bill retorts by arbitrarily requiring 3 or 4 Lucas tests,

I have more pseudoprimnes, in waiting, with which to reply.

In any case, he is doomed, by the absolute Pinch, as given in (4).

David