[quote=R.D. Silverman;141695]It would have proceeded much more slowly. So what?
The actual numbers themselves [B]are not important[/B]. It doesn't
really matter whether we know 38 Mersenne primes, or 39, or....
It is the [B]techniques[/B] that are interesting, and what we learn
implementing them.[/quote]

I agree, mostly. The greatest accomplishments here were the development of the technique (Crandall) and its implementation (Woltman). However, being an engineer I am perhaps somewhat biased toward developing a technique or device *for a purpose*. One of the most obvious purposes of the IBDWT is for speeding up primalty proving. Dr. Crandall says as much in his original paper. George's purpose is obvious too: to find as many Mersenne primes as fast as possible. Why invest all that time to create a brillant program and make it freely available if you did not want as many people as possible to use it?

Maybe I'm way off base, but I imagine that Dr. Crandall and George are thrilled by the EFF prize, because it puts their work in front of so many people. Furthermore, I bet that a great many more people today are at least a little bit smarter about number theory, fast algorithms, etc. then would be with no prize. I agree that it is depressing that a prize is necessary to get some people to pay attention to such things, but it is the way it is.

I view the prize as activism, same as in politics. If I want people to pay attention to my favored candidate, I will probably have to spend time and money to make it worth the while of enough people. Same principle here, only the candidate in this case is the accomplishments of the people involved - in the hopes that a few others are inspired to follow in their footsteps.

Long message shortened: there should continue to be a prize for some lucky person, in addition to the principals behind the scenes. It is a small price to pay for the knowledge that is passed on through the project and the for the popularization of a subject that otherwise would not get much attention.

- ben.

[QUOTE=bsquared;141719]

<snip>.

- ben.[/QUOTE]

"The purpose of computing is insight, not numbers"

[QUOTE=R.D. Silverman;141717]In the beginning, to test algorithms and implementation of the same.
Now, however, it has become more or less just recreational.
Which is [b]fine[/b]!!! But I see no justification for awarding
$$$$ for just a recreational activity.

If the purpose of the money is to spur new research, then it
should be offered for (say) finding an IMPROVEMENT in the algorithm,
or perhaps a new insight into the theory of how M_p's are distributed,
etc.

Participating in GIMPS for recreation is fine. But then the money
becomes an anathema. It should be a labor of love, [b]IMO[/b].

I would not even feel a 'thrill of discovery', if I were to find a
record prime, [b]unless[/b] I were running my own code or (say)
testing a new method. Similarly, I would not feel particular pride
in a new record factorization [b]unless[/b] it were based on a new
algorithm or an improvement on an existing algorithm. Otherwise,
it is just a matter of throwing more CPU time at a known algorithm.

Oliver Atkin once called the Cunningham Project "Wagstaff's Stamp
Collection". He also said that it was a distraction from doing real
math. I participate because of factoring's relevance to RSA, because
I am constantly working on improving my code and looking for ways
to improve the algorithm, and because I promised Dick Lehmer that
I would push to finish the base 2 tables....

I see the GIMPS project in somewhat the same way... It is a stamp
collection; a recreation. I do not run GIMPS code because it is not
mine, and I have nothing to offer in the way of theoretical improvements.[/QUOTE]

I'm satisfied with this answer, I stopped running the GIMPS client years ago for similar reasons.

However, the prize money is not meant to further new research,

[quote=EFF]
The Electronic Frontier Foundation (EFF), the first civil liberties group dedicated to protecting the health and growth of the Internet, is sponsoring cooperative computing awards, with over half a million dollars in prize money, to encourage ordinary Internet users to contribute to solving huge scientific problems.[/quote]

it's to get average people to contribute. At this point, I suspect we're going to have to agree to disagree, because I think they have every right to throw this money where they choose to throw it (and I think it is beneficial). I think that putting prize money towards developing a new algorithm is better in theory, but the people capable of developing new algorithms almost never seem to be motivated by prize money, in my estimation.

Personally, I'm more offended by the notion that a person's name is attached to the discovery of a prime just because their computer was running that lucky number. Money is a cute little carrot, recognition is forever. (cf. L'Hospital)

[quote=R.D. Silverman;141717]
...
If the purpose of the money is to spur new research, then it
should be offered for (say) finding an IMPROVEMENT in the algorithm,
or perhaps a new insight into the theory of how M_p's are distributed,
etc.
...
[/quote]

The vast majority of people are *not* techniquely capable of doing either of these things. The people that are capable will be motivated to do so with or without the possibilty of a prize. What the prize does bring to the table is an increase in the probability that new people will be inspired to learn what it takes to do these things. In other words, helping to create a new generation of talent in the field. You yourself have advocated for just that in this forum multiple times in the past.

[quote=R.D. Silverman;141720]"The purpose of computing is insight, not numbers"[/quote]

Agreed 100%. See the immediately preceeding post.

Poisson process, with 1/e^gamma slope
 

[QUOTE=R.D. Silverman;141695]It would have proceeded much more slowly. So what?
The actual numbers themselves [b]are not important[/b]. It doesn't
really matter whether we know 38 Mersenne primes, or 39, or....
It is the [b]techniques[/b] that are interesting, and what we learn
implementing them.[/QUOTE] Bob, knowing more Merseonne primes is also interesting in order to check if the observed repartition of Mersenne primes is following the expected (but not proved) Poisson process, with the 1/e^gamma slope. Based on my computations, it seems good ! (but wait for Chris Caldwell to publish a new version of his "Where is the next Mersenne prime ?" page).
Tony

[QUOTE=R.D. Silverman;141695]It is the [b]techniques[/b] that are interesting, and what we learn implementing them.[/QUOTE]Verifying these numbers with big machines with many cores is also a way to measure how efficient are both the software FFT-parallelizing techniques and the machine scalability.
By the way, I'm gathering informations about the scalability of Glucas (maybe Mlucas some day, when Ernst has finished his asm work and can move to something else) on different machines, like a 2x 4cores Harperton, a 64x Power6, and (cross fingers !) a proto of Nehalem 8 cores !
Tony

Status of my verifications
 

Prime of 23th of August: nearly 76% done.
Prime of 6th of September: about 37% done.
I'm late, I'm late... Need a new super-computer...
Tony

[QUOTE=T.Rex;141735]FFT-parallelizing techniques and the machine scalability.[/quote]

This is probably the cutting edge of Mersenne research now. Maximizing the efficiency of parallel FFTs would have wide-spread benefits. Will we (Ernst, myself, Guillermo, Tony, etc.) be the ones to make improvements in the area? Maybe, maybe not, but it does show why continuing a "not important" search for Mersenne primes could turn out to be unexpectedly useful.

[quote]a proto of Nehalem 8 cores[/QUOTE]

Nehalem has me worried. The 256K L2 cache is rather small for prime95.

Actually Bob, there is one thing you might be able to do to help Gimps.

The current factoring implementation used by Gimps is based on finding small factors of (Mp) numbers. There is no current efficient implementation of a factoring algorithm that works near the sqrt (Mp). You might look at an efficient method of coding such an algorithm. Please note that I am not refering to ECM or P-1 in this statement.


DarJones

Do I hear thunder in the distance?