-Since the test is an indirect one we do not test the p. suspect

itself.What we do by programming the failure functions is just to

check that the functions do or do not cover the relevant x value of

the suspect. If x is covered it is composite if not it is prime.The

logic:

Every time f(x), in the case of x^2 +1 or x^2 + x +1, is composite

one of its factors is less than x; hence it must be generated by one

or more of the failure functions. In other words the method is like

a sieve. Trust this is clear.

-- In

primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>

wrote:

>

> --- On Tue, 8/5/08, dkandadai <dkandadai@...> wrote:

> > Phil has replied to me saying that perhaps a counter-example

> > to the

> > indirect p.test can be found.I had replied " I hereby

> > challenge anyone

> > to produce one". He has requested me to make it

> > public. In my latest

> > reply to him I was perhaps a bit rude for which I feel

> > sorry.

> > Anyway my challenge stands.

>

> You need to first prove that it is actually primality test rather

than, for example, an exponential-time factoring algorithm. The

latter would be of no interest to anyone.

>

> Phil

>