Fanjita and co have done what many thought to be impossible. Today Noobz have released the first-ever, working homebrew on all firmwares! Yep, that includes even firmware 3.50.
"Based on Lumines, the "Illuminati" exploit is a user-mode exploit using a buffer overflow in the savedata file - similar to the GTA exploit."
So if you've got a copy of Lumines (the UMD disc), then you can run homebrew on your PSP, no matter what the firmware version is. Currently, the only homebrew compatible with 3.50 is this Hello World demo, but in the future Noobz intends to release a new HEN and downgrader!