[Not in reply to any specific message - no names, no pack drill]
Hey, guys, surely we don't want a war over this?
Here are a few relevant points:
1. GIMPS/PrimeNet as a whole constitutes a "team" in so far as we
(usually) co-operate loosely with each other in order not to waste
time and effort needlessly replicating each other's work.
2. However, it is certainly the case that (a) at present, the first
LL test is run by a single individual or team operating their
computer system(s) independently of GIMPS/PrimeNet, and (b) at
present, the only thing which participants to GIMPS/PrimeNet have
agreed is that they will be listed along with George & Scott as co-
discoverers in the event that a Mersenne prime is discovered.
Run this through the courts if you must (assuming you have endless
time & money to waste) but I think most juries would conclude that
the prize money should be awarded to the individual discoverer, in
the remote chance that any was left after the lawyers had taken their
slice.
My guess is that making participation to GIMPS/PrimeNet conditional
on agreeing to share the prize would be A Big Turn-Off. Though I'm
equally sure that the vast majority of participants would indeed
share out any award in some more or less sensible way, even in the
absence of "guidelines".
I certainly agree that some of the "shares" suggested should exist,
but perhaps we need to fund them in a different way. (I've already
pledged $500 towards a prize fund for discovery of any Mersenne prime
which _doesn't_ qualify for the EFF award).
As for some of the other points mentioned:
Searching for Proth primes is less efficient than searching for
Mersenne primes, this is likely to remain the case unless/until
someone comes up with a "free" way of executing the remaindering
operation modulo k*2^n+1. Also, since there are two parameters to
play with, it's going to be harder to coordinate. The positive sides
are that there is almost certain to be a 10 million digit Proth prime
smaller than the smallest 10 million digit Mersenne prime, and that
there are some values of k which seem to yield higher densities of
primes than Mersennes (though, equally, there are other values of k
for which it is proved that no primes exist).
The other LL testing programs available are a lot less efficient than
Prime95 and its derivatives. This may change, in time, but it really
is dependent on someone with the time and expertise putting in a lot
of effort.
If anyone really wants to start testing 10 million digit Mersenne
numbers now, I would at least urge them to obtain exponents from
George, in order to prevent unneccessary duplication of effort. [If
George can't be bothered, I'll volunteer to do this task!]
Some commercial or adacemic research organization may well claim the
EFF prize. In fact, I think this is quite likely for the $100K prize,
and almost certain for the bigger prizes. The likes of Sandia already
have quite sufficient "clout" to make our effort pale into
insignificance, if they put their mind to it. Also, it may have
escaped your notice, but IBM (who _still_ have good labs & lots of
working capital) recently took over Sequent (a specialist in multi-
processor systems). What would be a better demonstration of the power
of this particular merger than a system powerful enough to test
enough 10 million digit Mersenne numbers rapidly enough to win the
prize, even though such a system would certainly cost more than
$100,000 to build?
There is one other relevant point, which comes back to the value of
encouraging co-operation. At present we find approx. 1% of the LL
test results submitted are incorrect. Assuming that these are due to
random errors, the proportion of incorrect results will increase with
run length. By the time we get to exponents in the 10 million digit
range (with run times of the order of a year) the error rate may well
exceed 10%. To avoid wastage of too much time, it will be valuable to
do something like issuing each exponent to two users and having
automatic cross-check points during the run (instead of just at the
end). Essentially this is just a refinement of double-checking in
tandem with first tests, but, if we adopt this, we will surely have
co-discoverers (in addition to George and Scott)? If we choose to do
this, we will _have_ to get users to accept a condition forcing them
to share the prize between them. In which case I don't see that it
matters much whether the two users whose computer systems did the
calculations split 50:50, or whether it's split 40:40:10:10 with the
smaller shares going to George & Scott. But I think that trying to
make the smaller shares any bigger than that would tend to cause
problems.
Sorry if the above seems rambling & inconclusive. It _is_ a difficult
problem, and I personally have difficulty in coming to any definite
opinion, except that the EFF prize certainly isn't worth destroying
the cooperative nature of the project over.
Regards
Brian Beesley
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