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-   -   Factored vs. Completely factored (https://www.mersenneforum.org/showthread.php?t=17051)

aketilander 2012-08-08 12:23

Factored vs. Completely factored
 
In the GIMPS database we can only see if an exponent is "Factored", but it can be difficult to find out wether it has been completely factored or not. On my wishlist is a status called "Completely factored" for those exponents which are proved to be completely factored.

You can find the completely factored Mersenne expos here:

[URL]http://www.garlic.com/~wedgingt/factoredM.txt[/URL]

So, if I understand it rightly M1061 (now M1277) was previously the smallest expo without know factors, but M929 is yet the smallest exponent which is not completely factored.

alpertron 2012-08-08 13:27

For some larger exponents, it is possible that the Mersenne numbers have been completely factored, but we will not be able to prove the primality of the cofactor.

ixfd64 2012-08-08 15:12

I came up with a [url=http://www.mersenneforum.org/showthread.php?t=13226]similar suggestion[/url] two and a half years ago. I agree that there should be some distinction between a fully factored number and one that merely has known factors.

aketilander 2012-08-08 15:34

[QUOTE=ixfd64;307353]I came up with a [URL="http://www.mersenneforum.org/showthread.php?t=13226"]similar suggestion[/URL] two and a half years ago. I agree that there should be some distinction between a fully factored number and one that merely has known factors.[/QUOTE]

There is really one small thing which may complicate the whole a little. We also have some "almost" fully factored expos, in the sense that the last factor is a PRP but not proven to be prime.

Dubslow 2012-08-08 18:09

I would say that while PrimeNet is lacking in such functionality, you can use the FactorDB to check if a Mersenne number is [URL="http://factordb.com/index.php?query=M1277"]fully[/URL] [URL="http://factordb.com/index.php?query=M929"]factored[/URL] or not.


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