Glenn Brown writes:
The computer has found TWO factors of 2^647+1. It's still
searching! WHY
Good question. Most likely, because what's left is still composite.
But since I don't know what program you're using nor what factors it
has found, I can't help you more without more information. From the
current lowM.txt file, which presently includes all the data that I
have on incompletely factored Mersenne numbers with exponents up to
200,000:
M( 1294 )C: 4570409
M( 1294 )C: 9021769
M( 1294 )C: 932184694939
... since:
(2^647 + 1)*(2^647 - 1) = (2^647)^2 - 1^2 = 2^1294 - 1 = M(1294)
... factors of 2^647 + 1 will be listed under M(1294) in lowM.txt.
Factors of M(1294) that are also factors of M(647) are only listed
under M(647). Data for completely factored Mersenne numbers is moved
from lowM.txt to factoredM.txt.
LowM.txt - factors, cofactors' primality, etc. - is verified by the
ecm3 program of the mers package every time I update my data, usually
for all exponents up to around 15,000 (depending on how long I let it
run).
New data is gathered from George Woltman's ftp site, Paul Leyland's
Cunningham Project ftp site, and Conrad Curry's P-1 data ftp site
automatically as part of my update scripts.
Will
http://www.garlic.com/~wedgingt/mersdata.tgz tar'd gzip'd lowM.txt, etc.
mersdata.zip DOS zip'd lowM.txt, etc.
mersfmt.txtdescription of format
mersenne.html descriptions and links
