## Phil.s speculation

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• 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
Message 1 of 3 , Aug 4, 2008
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.
Devaraj
• ... 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
Message 2 of 3 , Aug 5, 2008
> 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
• -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
Message 3 of 3 , Aug 5, 2008
-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:
>
> > 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
>
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