Scientific goal

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Profile [AF>Dell>LesDelliens]La frite
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Message 68 - Posted: 1 Apr 2010, 20:32:51 UTC

Hi!

Would it possible for you to explain briefly what is the current scientific goal of the project please?

Because all I can see as news is this sort of stuff:
"12-digit factor of P2203 has been found ?? times"
What is this P2203? what's the point of finding so many times the same factor??

Thanks for your explanations

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Message 69 - Posted: 2 Apr 2010, 6:27:10 UTC - in response to Message 68.
Last modified: 2 Apr 2010, 10:34:07 UTC

(Thanks for your post)
In a nutshell, to find (new) factors of Mersenneplustwo numbers, with the WEP algorithm.
(pls feel free to follow up requesting more detail on this if required - I believe I still have a record of some text that was posted on another newsboard explaining the WEP algorithm in a bit more detail...)
Edit: This thread _may_ be helpful: http://mersenneforum.org/showthread.php?t=5735
P2203 is the Mersenneplustwo number formed by adding 2 to the Mersenne prime, 2^2203-1.
There is no intrinsic value to finding any factor more than once (as you might guess). The reason for keeping a record of number of times the 12-digit factor is found, is so that, when (hopefully!) we find bigger factor(s) we can gauge how efficiently these bigger factors are found relative to the smaller one(s), and thus show that the WEP algorithm is working as hoped.
J
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Profile [AF>Dell>LesDelliens]La frite
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Message 70 - Posted: 2 Apr 2010, 15:20:12 UTC

Ok so if I understand well the goal is double:
1)find factors of P2203
2)prove a certain type of complexity of the algorithm through the analysis of the number of times each factor is found depending on its number of digits.

If so, how many factors have been found for the moment for this number?

Thanks for responding so quickly!

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Message 71 - Posted: 2 Apr 2010, 17:08:22 UTC - in response to Message 70.

Exactly those two points - you summarise the dual-nature of the goal(s) well. [though of course, being optimistic, if P2203 is successfully completely factored, then we could move on to P2281, P3217, ... etc.]
To date, only the 12-digit factor (208613913329) has been found.
J
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Profile [AF>Libristes] nico8313
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Message 72 - Posted: 2 Apr 2010, 17:17:16 UTC - in response to Message 71.

Hi

Thank you for this explanation
is nice

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Message 228 - Posted: 23 Sep 2014, 13:20:16 UTC - in response to Message 72.

So... the project is endless then?
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Message 229 - Posted: 23 Sep 2014, 15:30:22 UTC - in response to Message 228.

[assuming your question is not rhetorical! :)]
(1) The project: "Factorize all the Mersenneplustwo numbers" is endless, yes.
(2) The project: "Fully factorize (M+2)2203" is finite.
(3) The project: "Find a new factor of (M+2)2203 by WEP" is finite, and (hopefully!) < (2) above.
(Thank you for your crunching, and for taking the time to read about the scientific goal, and post in the relevant place)
J
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The Physicist!
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Message 278 - Posted: 31 Dec 2015, 13:06:00 UTC

It is funny how I was asking myself the same question.
I just joined the project but I could not grasp exactly its goal.
Looking forward to helping and contributing to it.
Running from a Macbook Pro, i5 @ 2.4 Ghz (OSX Yosemite)

Cheers!
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Message 296 - Posted: 18 Sep 2016, 2:57:30 UTC

Why has the same factor been found so many times? I don't know how the WEP algorithm works, but it would seem that finding a factor once would be enough. If every workunit is running a different part of the search space, it seems strange that the same factor can be found multiple times.

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Message 297 - Posted: 18 Sep 2016, 10:36:23 UTC - in response to Message 296.

Hi jon b.
(Thanks for your message)
Pls see earlier in this thread for why we continue to find this factor multiple times.
As to why we find it so often, the smaller the factor, the more times we will find it across the search-space, and this one we're finding (so far?!) is only 12-digits, so it crops up relatively often.
HTH,
J
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Message 298 - Posted: 18 Sep 2016, 11:30:10 UTC - in response to Message 297.

...to expand further, and a bit more mathematically:
The WEP algorithm, like most other factorization algorithms (eg ECM), finds factors independently of each other, so "leaving this factor in" does no harm (I'm pretty sure) and gives us a useful secondary yardstick in addition to just a raw measure of the total number of wu's processed.
Across the whole search-space, accessed by a randomly distributed base, or seed, the factor crops up multiple times because, as Euclid showed, gcd(a, b) = gcd(a, a+b) = gcd(a, a+2b) = gcd(a, a+3b) etc...., and the final step in the WEP algorithm (again like a lot of factorization algorithms) is a GCD of two numbers.
J
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Message 300 - Posted: 4 Oct 2016, 19:46:40 UTC - in response to Message 298.
Last modified: 4 Oct 2016, 19:47:05 UTC

That makes sense. Also, doesn't the existence of one factor imply the existence of a second. When you say that "To date, only the 12-digit factor (208613913329) has been found" wouldn't that also mean that (P2203)/(12-digit factor) has been found as well?

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Message 301 - Posted: 5 Oct 2016, 9:23:37 UTC - in response to Message 300.

Yes, you're absolutely right! I guess I was talking _prime_ factors :) [which is quite a common distinction]
J
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Message 305 - Posted: 19 Nov 2016, 11:09:59 UTC

On trying to get to the bottom of the purpose of this project I seem to be going round in circles. I get the impression it is an inefficient, pointless, vanity project that will never conclude anything useful other than the gullibility of volunteer contributors like me.
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