Thanks is a poor word, but anyway thanks to all.
 
I will move on, though my first idea such like: 
 
   2kp+1 is a factor when k is 2^x
 
is already dead at M37. :-( damned!
I will find another proposal, prove it or disprove it, and continuing
getting new ideas. 
 
It seems to me that this k (in 2kp+1) is never:
 
  4,12,20,28,36,46,52,60,68,76,84
 
at least for less than M416.947.
 
Am I again a fool for a pattern already proved?
 
 
On the other site you can watch this:
 
k=2, 1875 factors in above mentioned space up till M416.947 spanding
35144 primes:
k=4, 0
k=6, 1132
k=8, 715
k=10, 465
k=12,0
k=14,233
k=16,351
....
k=32,138
...
k=64, 65
...
k=72,123
k=74,33
 
remark, the overall high values of k=2^x factors and remark the low
value of eg. k=74. 
Also remember these factors where obtained by prime95 Advanced factors
first of all looking for a low or maybe the lowest value for the factor.
So my point here is chance of  k=2^x for a factor is high, espcially
when p95 has run to the end regarding 64-70 bits low facoring and not
found a factor.
 
Now am I wrong in this conclusion and should I drop the the project or
is still a small amount of light passing through the halfopen doorway?
 
br
happy hunting
tsc
 

 

        
           Try Will Edgingtons's page,
           http://www.garlic.com/~wedgingt/mersenne.html .
           Use used to keep a comprehensive archive of known Mersenne
factors. I am
           not sure how up to date this files are, but it is a good
starting point.
        
        I still keep the data, but have not had time to update the
online
        copies for a while now for several reasons that have nothing to
do
        with GIMPS or other Mersenne stuffs.
        
        

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