> On 4 Nov 99, at 20:37, Preda Mihailescu wrote:
>
> > Sorry to contradict you, but this things are called ``deterministic under the
> > ERH'', which is totally different from deterministic, straight.
>
> Of course, you're right.
>
> > Simply, if the ERH
> > is proved one day to be true, all the effort spent meanwhile for finding
> > deterministic primality proofs [independent of the ERH] would look
> > rather curly. But such is life.
>
> [Phrase in brackets is my insertion - BJB]
>
> Not neccessarily. Work applied in one direction sometimes proves
> useful somewhere else, even if the original project fails or is
> superceded.
>
Of course, of course. I said curly, funny, etc. I did not say condemned in the
next 25 eternities to bogus treatment, or something. Nuances !
> > I was in Rome this summer when the proof of the Taniyama conjecture
> > was announced, and at the same conference, in fact the day after the
> > announcement, there were several talks about ``elliptic curves which
> > are modular'', or ``Weyl curves'' - which were in that day known to be
> > simply all elliptic curves :-).
>
> It's unfair to expect people to rewrite their papers overnight!
The same thing ! Where is your humour ? No one expects nothing from
anyone - but it would hypocritical to claim that the situation of those
people was not funny/embarassing/out of common - you chose the word
the pleases you most !
>
> > And as for your claim that Miller's proof would feature a contradiction to the
> > ERH, that is also false.
>
> If we find a number with a certificate of primality derived from some
> method not dependent on the ERH but which nevertheless passes
> Miller's Test as a strong pseudoprime for all bases less than
> 2(ln n)^2, then either Miller's paper is broken, or we have a
> counterexample disproving the ERH. So far as I'm aware, Miller's
> paper is no more contentious than Pythagoras's Theorem.
>
I would say Miller paper is correct. In fact not only is it quite old and resisted
scrutiny, but first of all the ideas are rather simple, so it is difficult to hide
a reasoning bug behind them. (E.g., you cannot compare to Wiles 220 pages
proof, which took a time to be followed and understood). So yes, it would
be a counterexample to ERH.
> Proth's Theorem allows us to find certified prime numbers of a fair
> size (thousands of digits) quite rapidly. Granted these are a very
> thin subset of all numbers, and, even then, running sufficient
> Miller's Tests on a number with "only" a thousand digits would take a
> very large amount of CPU time. That's why I won't be holding my
> breath!
>
No one is out for your holding your breath. ( I do not realle understand for what
either,
but it is unimportant).
Regards
Preda
>
> Regards
> Brian Beesley
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