The worth or futility of factorizations relating to OPNs
 

[QUOTE=R.D. Silverman;278238]No retraction either. These calculations to extend the lower bound on OPN's are pointless.[/QUOTE]

There you go again. You can't remember what we are talking about.

In post #709 you said the factorization of 811^71-1 was pointless. I challenged that. That is the on-topic part of our discussion. You can't stay on the topic - you keep rambling off into discussions about the OPN search, the glory of pushing the leading edge, and your perceived persecution. I ignored your off-topic meanderings - your views on these things are well known, you said nothing new, I have responded elsewhere. I kept insisting we return to the topic - is the factorization of 811^71-1 pointless? In post #721, in the midst of additional off-topic meandering, you admitted that individual factorings are not pointless. That is a retraction of the only topic I have engaged you in on this thread. Apology accepted for the retraction that was made.

[QUOTE=R.D. Silverman;278251]It is one thing to work at the leading edge in order to improve factoring methods and code. It is another just to use the tools written by others to do computations that have little use. [/QUOTE]

Isn't this the obvious and natural result of your work? Why do you push the boundaries? You made this possible. You and Moore's law created the world where factoring 811^71-1 is possible with minimal comprehension. While we live here happily, you are creating the world where factoring even larger numbers with even less comprehension will be possible. In a few years we will be living in that world while you are creating the next one.

[QUOTE=em99010pepe;278254]No one tells me what to run when I pay for my electricity bill. If I run for fun or whatever goal it is my problem, not yours. We don't need someone to tell us what we should run.
Personally I think all factoring projects are bullshit, we should be saving energy but most of us do it for fun.[/QUOTE]

Did you have this same attitude toward your professors in college when they
told you that something was a waste of time? Or that you should focus on
some particular subject as opposed to another?

You can indeed do whatever you please. Go right ahead. It is your
electricity.

And it is my right to suggest that these computations are pointless.

As for all factoring projects being worthless: Your opinion isn't worth very
much; RSA is used by everyone on the Internet. Knowing the state of the
art and continuing to push the state of the art is important so we can
keep track of the security of RSA. [if for no other reason]. The only
real reason why the Cunningham project is useful is that historically it has
been used as a standard for benchmark data for pushing the art.

[QUOTE=Zeta-Flux;278268]And this is the key to the issue. These factorizations are not merely raising lower bounds. They are computations which have either directly aided in new mathematics,
[/QUOTE]

No, they have NOT. The mathematics stands on its own, independently
of any computation.

[QUOTE]
or given an example of that new mathematics in action.
[/QUOTE]

The way to demonstrate the utility of the math would be to apply it to
EXISTING data so see how much value was present in the math itself.
Showing that the math could raise the bound WITHOUT the need for
more computation would enhance its value.

[QUOTE]
They also help us get a better grip on the problem, by giving us more examples on which to make conjectures.[/QUOTE]

Ah. So please tell what conjectures have arisen from these 'more
examples'.

William, you know I love it when you get angry:smile:

David

[QUOTE=akruppa;278269]You were banned for habitually insulting people for several years ("imbecile," "moron," "idiot" to name just a few words you used). The insult against Garo was the straw that broke the camel's neck. If I see an insult worthy of moderation in this thread, I'll act on it, don't worry.

Edit: any further discussion of the worth/futility of these factorizations is to be taken to the Soap Box forum, [url]http://www.mersenneforum.org/showthread.php?t=16235[/url].[/QUOTE]


Technical discussion of the worthiness of research projects is inherently
part of the process. People submit research proposals all the time. Many
are turned down or judged to have little value.

Research best takes place in a free and open forum in which participants
are free to discuss the merits of the research itself. Your banishment
to the soapbox clearly shows YOUR bias and is an anathema to the process.

I have yet to see a cogent reply to my criticisms. Or can it be that
the participants can give no technical justification? Noone has yet
said exactly what they hope to [i]accomplish[/i] or where the value
lies in such purported accomplishment. If they answer that they are
indeed trying to raise the OPN lower bound, they need to say where
the value lies in doing so.

Neither is this forum a techical journal, nor are you a referee here. You voiced your opinion before, repeatedly. We are well aware of it and choose to disagree. You say these postings annoy you? Someone posting something you don't find very interesting on someone else's forum annoys you? Don't you have anything better to do than be the old lady with the spyglass?

[QUOTE=wblipp;278270]There you go again. You can't remember what we are talking about.

In post #709 you said the factorization of 811^71-1 was pointless.
[/QUOTE]

You keep trying to put words in my mouth. I said "pointless"
within one particular post that was part of a SERIES OF POSTS.
You keep assuming that because I only replied to ONE post, I only
referred to one post.

Next time I will add the words "pointless" to EVERY post
to satisfy you. It is redundant, but you seem to want that.

The subject under discussion is whether there is any technical merit
in these endless mundane computations to chase OPNs. You (and others)
keep avoiding this issue. And you keep trying to change the real subject.

[QUOTE=akruppa;278276]Neither is this forum a techical journal, nor are you a referee here. You voiced your opinion before, repeatedly.
[/QUOTE]

And as long as people feel the need to post these results, I will continue
to post my opinion.

[QUOTE]


We are well aware of it and choose to disagree. You say these postings annoy you?

Someone posting something you don't find very interesting on someone else's forum annoys you? Don't you have anything better to do than be the old lady with the spyglass?[/QUOTE]

It works both ways. Don't the people who keep posting these results
have better things to do than to repeatedly:

(1) Blindly keep running software that was the brilliant work of others?
-- while making no contribution to that software except criticizing
how it works?
(2) Keep posting numerical results of little real value?

It is the computer equivalent of "couch potato". Just use the technical
accomplishments of others while making no original contribution to
the art. We all watch TV. Very few know its inner workings. Nor do
we need to know in order to watch. But we don't pretend that our TV
watching has value other than entertainment value. And we don't need
to make internet postings that say 'Hey! Last night I watched the Simpsons!'

[QUOTE=R.D. Silverman;278280]It is the computer equivalent of "couch potato". Just use the technical
accomplishments of others while making no original contribution to
the art. We all watch TV. Very few know its inner workings. Nor do
we need to know in order to watch. But we don't pretend that our TV
watching has value other than entertainment value. And we don't need
to make internet postings that say 'Hey! Last night I watched the Simpsons!'[/QUOTE]I can see you're not one of the Twitterati. You'd be surprised at just how many of such inanities are posted by so many every day.

[QUOTE=R.D. Silverman;278273]No, they have NOT. The mathematics stands on its own, independently
of any computation.[/quote]This is demonstrably incorrect. I have made advances in the mathematics directly as a result of doing many, many, many mundane computations. Occasionally, the best way to help others understand those advances is to have them work through a few of those same mundane examples.

Furthermore, I would argue that a paper where an author states an improvement in the mathematics which can finish off a problem with a little easy computation is not complete until those easy computations are done.

For example, using some straightforward heuristics it is easy to show that odd perfect numbers must be divisible by a sixth power of a prime. However, nobody was able to prove it. Working with an undergraduate over the last two years, Ochem and I discovered a way around the previous roadblocks when there is a small prime factor. We also found a way to significantly improve the upper bound on the smallest prime factor using sieve methods. Yet, in my honest opinion, the paper would have been incomplete if we left it at that stage. To finish, we then had my undergraduate researcher do some rather tiresome but necessary computations to show that the smallest prime factor cannot be less than 10^7 (or something like that). In particular, we got rid of an incredibly difficult case, when the smallest factor is 5.

The method we used was new, and it was important not only to present the new idea, but to put it into action.

[quote]The way to demonstrate the utility of the math would be to apply it to
EXISTING data so see how much value was present in the math itself.
Showing that the math could raise the bound WITHOUT the need for
more computation would enhance its value.[/quote]The point is not merely to raise the bound. That is just a side benefit of these computations.

[quote]Ah. So please tell what conjectures have arisen from these 'more
examples'.[/QUOTE]Specifically with regards to odd perfect numbers, one conjecture that has arisen is that Euler's special prime might have to be the largest prime divisor (and be raised to only the first power). This is born out by Descartes' spoof odd perfect number, and a large number of other computations where this becomes the most difficult case.

I was also led to conjecture that the OPN problem may be related to the fact that \gcd((p^a-1)/(p-1), (q^b-1)/(q-1)) has very few large prime factors, unless a or b is extremely large.