The statement was not exactly formulated :

if f>1 is the smallest factor of a Mersenne number, than there exists a n0>1 for the function f(n)=2n²-1

where n0 is the minimum, so that f | f(n0) and

__maximal__ one prime g with f*g=f(n0) where g<f

This statement would allow to limit the recursion deep of my algorithm.

Thanks if you spend me some lines.

P.S. I did some programming but the runtime has to improve further.