Factored vs. Completely factored

aketilander · 2012-08-08, 12:23

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:

http://www.garlic.com/~wedgingt/factoredM.txt

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 similar suggestion 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:

Originally Posted by ixfd64

I came up with a similar suggestion 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.

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 fully factored or not.

2012-08-08, 12:23	#1
aketilander "Åke Tilander" Apr 2011 Sandviken, Sweden 2·283 Posts	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: http://www.garlic.com/~wedgingt/factoredM.txt 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.

2012-08-08, 15:12	#3
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 5×11×43 Posts	I came up with a similar suggestion 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. Last fiddled with by ixfd64 on 2012-08-08 at 15:12

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2012-08-08, 13:27	#2
alpertron Aug 2002 Buenos Aires, Argentina 17×79 Posts	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.

2012-08-08, 18:09	#5
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 1C35₁₆ Posts	I would say that while PrimeNet is lacking in such functionality, you can use the FactorDB to check if a Mersenne number is fully factored or not.