> Hi all,
>
> About a month ago I invited Meganet to show me their primality
> program, a small subcomponent of VME. Saul stopped by our office. I
> echoed the Mersenne list's skepticism, but suggested independent peer
> review might buy Meganet better credibility. I don't necessarily
> support Meganet's claims but thought being open minded enough to
> invite concrete results would clear the air.
>
This is a fair approach !
> I signed a simple NDA, the same that up to three other reviewers I
> choose will sign to try the program and examine/modify/compile the
> code. I have not yet received a copy of the source code, pending
> further progress on their patent application.
>
Basically, once an application has been announced, the idea is protected.
Did they already announce a patent at all or are they still working on the
claims ?
> He walked me through the code, explained the algorithm and described
> how it was developed with Milstein. The program was simple - a few
> pages - and uses a public domain integer math package. I'm tough to
> snow and didn't detect any B.S. as we reviewed its internals, but I'm
> no math expert, either.
>
> I can say, loosely, that the 'T-sequence' primality test is actually a
> family of four related complementary algorithms performed in series,
> any of which can reject a number as composite, but if all four pass
> the number is supposedly prime.
>
> One claim Saul made (and showed on paper to my unqualified eyes to
> verify) was that pinning the coefficients of the 'T-sequence' to a set
> of specific values causes it to degenerate into the LL series. Saul
> also claimed the algorithm detects and rejects strong pseudo-primes as
> composite, and showed some examples with the program (I don't recall
> what they were).
>
There are _very_ many ways to generalize Lucas - Lehmer sequences.
And I can also define on the spot a dozen generalizations of which I am
prety positive that no one might come up with an example of failure
(an adapted kind of pseudoprime that would pass the given test). The
point is that giving a proof is more than nobody in the next 100 years
not being able to show a counterexample. So I do not think very much
of the testing idea. If they combine four different tests in the LL flavour,
one may be smart enough to do so and making it _really_ hard for someone
to come up with a counterexample. This happened last year with a student
who made the same kind of claim public: he used two LL kind of tests, and
R.Pinch had a pseudoprime for _that_.
> >The number n=4^7057-3 has been proved prime by cyclotomy: with 4249
> >decimal digits, it is currently the largest prime proved with a
> >general prime proving algorithm. The main stage of the proof took 6
> >hours, the final "Lenstra - gcd and trial division" step (allowing a
> >factored part of O(n^{1/3}) took roughly 2 days.
>
> Luke invited me to try the Meganet program on 4^7057-3. It reported
> the number as prime in 33 minutes on my PPro 200, with a bunch of
> other apps going at the same time.
>
Sounds totally feasible for four extended LL tests ! They cannot take place in
too large extensions though ...
> I had planned to get the code before asking the list for a few folks
> interested in taking a crack at finding a flaw in it. We get only
> three evaluations under NDA. Maybe we can use one up to hook it up on
> a server under a web form in kind of constrained batch mode. Any
> takers? Please email me privately.
>
In short words: unless there is a crude programming error too - which I doubt, since
I believe they tried it on quite some known primes - it is _only_ the proof scrutiny
which can make the difference. It is simpler with factoring ....
Regards
Preda
> Regards,
> scott
>
>
>
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