On 5 Feb 2001, at 22:06, George Woltman wrote:
> >Maybe it would be useful to show a 64-bit residue after completion of the
> >probable prime test?
>
> True, but no one has volunteered to keep a central list of residues, much
> less organize a rigorous search of Proth candidates.
Is this really neccessary? I'd be more interested in what happens to
those candidates which pass PRP and go on to Proth, or PrimeGen. If
Proth finds "not prime" it doesn't tell you anything else. There is a
chance that something glitched. Presumably also the residue will
depend on which base you use for the Proth test, I'm not sure the
program always makes the same choice. Please excuse my ignorance.
However I certainly agree that the search needs to be organized
better before anyone starts worrying about possibly missing ~1% of
the primes in a "searched" range. I messed around with Proth a couple
of years ago, registered some ranges (the mechanism doesn't seem to
have changed since) and found 4 primes over 20,000 digits in a couple
of P100 CPU months - these were just about "top 500" at the time - of
which 2 turned out to be rediscoveries from someone else working on
the same ranges without bothering to register them. Not very
encouraging :(
When Proth does find a prime, it verifies it by a second test using
the same program on the same system but using a different base. This
doesn't "feel" as good as GIMPS/PrimeNet's independent double-
checking mechanism.
Incidentally, am I missing something? The Fermat test for
pseudoprimality (which is equivalent to a Proth test for true
primality, given a suitable candidate number and a suitable choice of
base) takes as long to run as a LL test on a number of the same size.
So, what test is PRP running? Obviously there's no point in running
Fermat's test with base 2 for Mersenne numbers, but I find it
somewhat less obvious that Fermat's test with base 2 would eliminate
a useful proportion of Proth candidates. If PRP is doing something
else, and runs significantly faster than Fermat's test, is there any
point in using it to pre-filter Mersenne candidates???
>
> >For now, it looks to me like GIMPS is the most reliable way of looking for
> >primes. Does anyone on the list have a view on this?
>
> Both are quite reliable methods for finding primes. One is good at finding
> good sized primes, the other good at finding record primes. BTW, the
> Proth program and OpenPFGW program could be used to find world-record
> primes. They are less than half as efficient as prime95 - but you get to
> test numbers that are much smaller than the M12000000 currently being
> assigned by Primenet.
Before June 1999 there was some discussion about using Proth to find
a million-digit prime for the EFF prize. Things may have changed
since, but I seem to remember that a new version of Proth was rushed
through to give it this capability, and even then the code used was
becoming distinctly marginal when testing numbers of that size. The
(semi-)organized use of Proth has concentrated on smaller numbers;
the biggest would be candidate Cullen prime numbers (p.2^p+1) with p
around 1 million, i.e. the order of 300,000 digits.
Robert's suggestion of using old, slow Pentium systems would make
very little sense if you were wanting to use Proth or OpenPFGW to
look for prime numbers around 2^7,000,000. The run times would be
just as long as LL test assignments using Prime95.
Regards
Brian Beesley
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