6.35,6.38,6.39 BUT NOT 6.37!
You will need:
6.20 update http://dl.qj.net/psp/firmwares/psp-firmware-620-update.html
PSP downgrader http://dl.qj.net/psp/homebrew-applications/639-downgrader-v31.html
6.20 CFW http://dl.qj.net/psp/homebrew-applications/cfw-620-pro-b8.html
Step 1: First things first
Also it says 6.39 but it still works on the others. Now place the PRO UPDATE (CFW) into PSP/GAME also. But if you want permanent psp cfw then put the permanent one into PSP/Game too.