Hi,
At 01:55 AM 2/6/2001 +0100, Robert van der Peijl wrote:
>So they could go for a prime of, say, formula k*2^n+1.
>They could run NewPGen to screen a range of numbers of that formula for
>small factors.
>Then run PRP to test each number in turn for probable primality.
>If it finds a probable prime, the Proth program could do the final and
>definitive test on that number. It all works really well.
For those unfamiliar with the Proth prime search, visit
http://www.utm.edu/research/primes/programs/gallot/
for more details.
NewPGen sieves out k*2^n+1 that have small factors, Proth
tests the remaining candidates for primality. About a year ago,
I wrote PRP, based on prime95's multiplication routines, to run
as an intermediate step to do a probable prime test.
I publicized the program on the primes mailing list:
http://groups.yahoo.com/group/primenumbers
Also, scan Chris Caldwell's excellent site for the OpenPFGW program
(grossly misnamed with my initials when Chris Nash did all the work!)
This tests the primality of other special forms of numbers again using
prime95's multiplication routines.
Using either of the above programs, it is relatively easy to find a prime
that cracks the top 5000 list at
http://www.utm.edu/research/primes/largest.html
>But what about the reliability of the result of each test in PRP?
>I'm wondering if PRP is about equally good at detecting errors during a
>calculation?
PRP uses the same sumout checks that prime95 does.
>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.
>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.
Regards,
George
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