A peaceful and pleasant night for you,

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

Is this a correct and (well known) logical statement ?

P.S. I am sure we find the next Mp before Christmas ...