Hi there, my Friends 
I'd like to share some results on the topic. So, for now, my "patient" has been RSA150 & algo is for searching Z...
Z == P + Q
N == P * Q
Current approximation reached 1.000044681307160289349497645265262062027290161287056271615916168525714076138289625709547909777477578645525505686636772954643946074847094002019290786349511024928454879317331762049771484736268086850579340310166395586498323803260792907800077463922559676313168204797474729443423059391492806223905521108490077250478
Src here https://sourceforge.net/projects/fastprimecruncher/files/FPC6.7z/download
Yet another remarkable result == FPC11 
S0T_guided doesn't provide more precision to estimate Z, but anyway result is rather curious...
number of loops: 100
0, 1, guided -'2' Please, enter version of S0T: 2
max Z to orig 0.6372928473642518323379782288209547690425255443149893931893843535970792784175827341996320445052560478699298601839443533476029251438056391372609841262742385638132526154494125575509613040804480112920323565670709588246405288404908622894629709445337
3438821172788817007077339573053851240563147377315517345065198070950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Mean Z to orig 0.847816521663485657814133837914497020755162842047555820546465597072997806836376666909889217573427171732060213664709636126472666235082149940337731722430296321900550428764812235598509955603712461573414220897963933429496883501654422702168241902579
76761323958691878245912386572902803522455618816353527839870935888620000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
min Z to orig 0.9899022558143058079156912361317448150859862978254655589273759906236828905373638276408135040588895053841490325450704413770152873445232075816563257398247839495905241594389007703128728139981129486315948151838363626365347525996501078194027536481540
9773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
closest Z to orig 0.989902255814305807915691236131744815085986297825465558927375990623682890537363827640813504058889505384149032545070441377015287344523207581656325739824783949590524159438900770312872813998112948631594815183836362636534752599650107819402753648
15409773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
number of loops: 1000
0, 1, guided -'2' Please, enter version of S0T: 2
max Z to orig 0.6372928473642518323379782288209547690425255443149893931893843535970792784175827341996320445052560478699298601839443533476029251438056391372609841262742385638132526154494125575509613040804480112920323565670709588246405288404908622894629709445337
3438821172788817007077339573053851240563147377315517345065198070950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Mean Z to orig 0.847254227884694871840210282646655859595988024436944967483139972442796707903333791436934964257186571865906945732866754293783827697653512151204043811848902883579696369741256577272607407808388339428622875723682619255196023276606284720922557147192
42324452492007603826245486175440403294895115476090344925759358260020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
min Z to orig 0.9899022558143058079156912361317448150859862978254655589273759906236828905373638276408135040588895053841490325450704413770152873445232075816563257398247839495905241594389007703128728139981129486315948151838363626365347525996501078194027536481540
9773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
closest Z to orig 0.989902255814305807915691236131744815085986297825465558927375990623682890537363827640813504058889505384149032545070441377015287344523207581656325739824783949590524159438900770312872813998112948631594815183836362636534752599650107819402753648
15409773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Number of loops doesn't affect output + ratio doesn't jump over 1.
src: https://sourceforge.net/projects/fastprimecruncher/files/FPC11.7z/download
