What does this really mean:
12-digit factor of P2203 has now been found by the project 359 times
Well the 12-digit factor is (literally) = '208613913329'.
The number we're testing is (M+2)2203 ie P2203, so this is one of the smaller factors already known. Now I'm _hoping_ (expecting?) a larger eg the 20-digit one, to show up at some point - or even an even bigger eg new one!! Because we're parallelizing the search for the purposes of the project, I'm using a random seed ie base for the algorithm (hence "random-base WEP algorithm&quot, which therefore explains why we find the smaller factors several times over for each instance of a larger factor. It's all best approached from the main M+2 homepage, with links to (Java) source code of my algorithm from there...
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Help Mersenneplustwo Factorizations[Link to official page - http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html ] (M+2) factor numbers two more than a Mersenne prime ie 2^p+1 when 2^p-1 is a prime. [Link to wiki][Link to (Google) discussion forum]
There is a close [mathematical] relationship to GIMPS [though the actual projects are otherwise unconnected], indeed each time GIMPS discovers a new Mersenne prime, one more target becomes available (it is even possible to use the GIMPS client to attempt factoring work for this project). Currently 15 out of 44 targets have been completely factored, and the largest (non-trivial) factor found to date has been 38-digits (of (M+2)9941).
There are several ways to participate in the project:
If you have internet connection, there is automatic work distribution of ECM factoring algorithm attempts via GMP-ECM (available for linux/windows/mac) and ECMNet (aka ECMclient).
If you have no permanent internet connection, then you can try one of the two other factoring algorithms (2kp-trial and WEP) presented at the site, for which java and/or native binaries (generally for most OSs) are available. Look carefully at the home page to see what progress has already been made before starting, or email the organiser to reserve a range.
[Or, if you're a prime-proving addict rather than a factorizer-guru, there are even prime-test candidates of residual numbers you could usefully test]. As I say, there are several ways to contribute
There is currently not an automatically generated work-credit page (though there is a rudimentary manually updated one) - it is hoped that the rare occurrences of finding a new factor should mark progress and credit. However, there is a WEP-Boinc client planned (which would use standard BOINC scoring system)...
The project is now 3+ years old, but the latest factor found to date, was a 19-digit factor of (M+2)13466917, on 2006-10-04 - so join in the hunt and see if you can land a 'monster'!
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One thing to point out - the Boinc project is still in ALPHA - if only because it is using a not-completely-proven algorithm at the moment. However this could be seen as an attraction, since it is therefore a chance to do some genuine cutting-edge research!!
Homepage of whole project (Mersenneplustwo) as above.
WEP-M+2 Project uses the WEP ("Wanless Extended Prime&quot [ie my own] mathematical factoring algorithm
to attempt to factor M+2 (Mersenneplustwo) numbers.
Mersenneplustwo numbers are those integers that are 2 more than a Mersenne prime (see GIMPS)
WEP is a new, and as-yet, not completely proven algorithm (though early indications, and (hopefully!) my theoretical understanding are promising). It is a derivative of WE specifically for Mersenneplustwo numbers - for which a significant speedup over general integers is possible.
The WE algorithm in turn, draws its inspiration from Fermat pseudoprime test, combined with "Wanless' Theorem - Fermat's Big Theorem" [link on my math website - http://www.bearnol.pwp.blueyonder.co.uk/Math/wanless.html] extension.
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