This PS3 Jailbreak 4.31 will work for all current versions of the PS3. This video shows you how to jailbreak PS3, on any firmware. To Jailbreak PS3, download the firmware above, and follow the directions below!
Direct download link: http://www.ps3jail.tk
STEP 1: Plug a USB stick into your computer
STEP 2: Create a folder in the root of the USB stick called PS3
STEP 3: Create a folder inside the PS3 folder called UPDATE
STEP 4: Move PS3UPDAT.PUP to the directory UPDATE that you just created on the USB stick
STEP 5: Plug the USB stick into your PS3
STEP 6: Navigate to Settings Tab
STEP 7: Choose System Update
STEP 8: Choose Update via Storage Media
STEP 9: It will say it found Version 4.31
STEP 10: Choose OK
STEP 11: Accept Conditions and Install Update
STEP 12: After less than a minute, your PS3 will update, beep 4 times then shut down.
STEP 13: Power up your PS3 (You will have to do it on the console and not by the controller)
STEP 14: Your PS3 is now jailbroken!
Direct link download: http://www.ps3jail.tk