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Old 2006-04-09, 22:17   #1
jasong
 
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"Jason Goatcher"
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Default Is there a simple way to track progress in Odd Perfect Number search?

Is there a simple way of tracking OPN progress? Not necessarily live, but it would be nice to know how much is being accomplished.

What would be really great, although not necessarily desired by an ecm server owner, would be a script that downloads basic information from the server, I'm guessing a small file. And then, either another program that can interpret it, or written instructions on how to interpret.

And, yes, I am trying to get a life. And, no, the attempt is not going the way I'd like.
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Old 2006-04-10, 11:10   #2
R.D. Silverman
 
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Quote:
Originally Posted by jasong
Is there a simple way of tracking OPN progress? Not necessarily live, but it would be nice to know how much is being accomplished.

What would be really great, although not necessarily desired by an ecm server owner, would be a script that downloads basic information from the server, I'm guessing a small file. And then, either another program that can interpret it, or written instructions on how to interpret.

And, yes, I am trying to get a life. And, no, the attempt is not going the way I'd like.
Yes. The progess on finding an OPN has been:

ZERO.

This will be the permanent status.
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Old 2006-04-10, 15:05   #3
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So you've finally found a strong heuristic (or even a proof) that supports your claim?

btw.:
You've misread his question. He asked about the progress of the project "OPN", not (your opinion of) the project's progress in finding an OPN.

Last fiddled with by Mystwalker on 2006-04-10 at 15:12
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Old 2006-04-10, 16:52   #4
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Quote:
Originally Posted by Mystwalker
So you've finally found a strong heuristic (or even a proof) that supports your claim?

btw.:
You've misread his question. He asked about the progress of the project "OPN", not (your opinion of) the project's progress in finding an OPN.
You miss the point. As usual.

Progress will always remain at zero until one is found. Then progress will
jump to '1'. I leave it to others to decide the likelihood of the latter
happening.

As for heuristics, Carl Pomerance has already given one.

We also have an algorithm (Brent) which allows us to keep raising the
bound. There is no theoretical reason why this algorithm can't keep
being repeatedly applied. Of course, it becomes computationally
prohibitive, but that is a practical obstacle, not a theoretical one.
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Old 2006-04-10, 17:13   #5
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R.D. Silverman,

With all due respect, I think you are the one who is missing the point. By "tracking OPN progress" it is probable that the initial poster meant something along the lines of "progress of the ECM-work for factorizations in the OPN project" or "number of factorizations left until the bound has been raised to >10^500." Finding an actual OPN would be an unexpected and wonderful thing, but the main purpose of the OPN project is to factor Cunningham numbers (with the side benefit of the very small possibility of an OPN popping out of the work).

Sincerely,
Zeta-Flux
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Old 2006-04-11, 02:05   #6
jasong
 
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Quote:
Originally Posted by Zeta-Flux
R.D. Silverman,

With all due respect, I think you are the one who is missing the point. By "tracking OPN progress" it is probable that the initial poster meant something along the lines of "progress of the ECM-work for factorizations in the OPN project" or "number of factorizations left until the bound has been raised to >10^500." Finding an actual OPN would be an unexpected and wonderful thing, but the main purpose of the OPN project is to factor Cunningham numbers (with the side benefit of the very small possibility of an OPN popping out of the work).

Sincerely,
Zeta-Flux
This is exactly what I meant.

Before my Linux machine kicked the bucket I could simply look at the screen and see how many curves were left for, for example, 3221^73-1. At the moment, all I know is that it's at the 55-digit level(Linux gives number of curves left, my Windows ecm program does not).

Your help is appreciated.
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Old 2006-04-11, 14:14   #7
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Quote:
Originally Posted by Zeta-Flux
With all due respect, I think you are the one who is missing the point.
Exactly - I thing he shouldn't answer questions that are not completely mathematically. The past has shown too many times that he is (intentionally?) unable to understand them.

Quote:
Originally Posted by R.D. Silverman
Progress will always remain at zero until one is found. Then progress will jump to '1'.
Wrong (but "black or white" seems to be your kind of thinking).
Depending on the interpretation, it *could* be true if "finding an OPN" was the only goal of the project...

Quote:
I leave it to others to decide the likelihood of the latter happening.
Actually, you didn't. You disguised your beliefs as facts, although even experts can't say for sure.

Quote:
As for heuristics, Carl Pomerance has already given one.
True, but no proof of non-existence.

Quote:
We also have an algorithm (Brent) which allows us to keep raising the
bound. There is no theoretical reason why this algorithm can't keep
being repeatedly applied. Of course, it becomes computationally
prohibitive, but that is a practical obstacle, not a theoretical one.
Interestingly, it seems like Brent himself "knows of no convincing heuristic and would not be particular surprised if [an OPN] should turn up".
Do you know more than he does?
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Old 2006-04-11, 14:51   #8
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btw.:
Could someone move all posts except #1, #6 and part of #5 to a separate thread? This off-topic talk again fills up the thread and makes finding the wanted answer a lot more difficult.

Last fiddled with by Mystwalker on 2006-04-11 at 14:52
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Old 2006-04-15, 02:12   #9
jasong
 
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I don't want to clutter the boards with my OPN questions, so I'll just put it here.

I don't have the education to understand the math behind the OPN stuff, but I don't think that's necessary for someone to answer my question.

Basically, I'm wondering if it's absolutely certain that a factorization will increase the lower bounds, or(and this might deserve to be a second question or topic) is it possible that a future factorization will give us a possible place to search for an OPN?

At one point I accessed a web page that explained the type of math used in OPN, but it would probably take me at least 2-3 weeks to figure everything out, and, unfortunately, I don't even know where to start.
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Old 2006-04-15, 04:44   #10
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Quote:
Originally Posted by jasong
Basically, I'm wondering if it's absolutely certain that a factorization will increase the lower bounds, or(and this might deserve to be a second question or topic) is it possible that a future factorization will give us a possible place to search for an OPN?
Every roadblock factorization could, in principle, lead directly to the discovery of an odd perfect number. If you look at the BCR Proof

http://web.comlab.ox.ac.uk/oucl/work...ub/pub116.html

Line 1 says "Suppose there is an odd perfect number divisible by 127, and suppose 127 is raised to the power 2. Then the odd perfect number must be divisible by 3 and 5419 because σ(1272)=3 x 5419."

Line 2 says "Suppose also that 5419 is raised to the power 2. Then 3, 31, 313, and 1009 must all divide the odd perfect number."

The proof continues like this, eventually reaching contradictions and backtracking to the previous assumptions. In principle the proof could, at any time, reach a set of assumptions which actually IS an odd perfect number.

Another way of saying this is that the boundary gets raised when we have exhaustively searched all possible ways to make an odd perfect number below the boundary - and there is the possibility that search will succeed.
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Old 2006-04-17, 00:13   #11
jasong
 
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Quote:
Originally Posted by wblipp
Every roadblock factorization could, in principle, lead directly to the discovery of an odd perfect number. If you look at the BCR Proof

http://web.comlab.ox.ac.uk/oucl/work...ub/pub116.html

Line 1 says "Suppose there is an odd perfect number divisible by 127, and suppose 127 is raised to the power 2. Then the odd perfect number must be divisible by 3 and 5419 because σ(1272)=3 x 5419."

Line 2 says "Suppose also that 5419 is raised to the power 2. Then 3, 31, 313, and 1009 must all divide the odd perfect number."
I don't have the education to understand that math, but thanks for answering my question.
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