A happy day for homebrew lovers with a PS3. After 7 years, a new exploit for PS3 has been released on Thanksgiving day of 2017 by PS3Xploit Team. This piece of software will enable the installation of any custom firmware on any PS3 that can be downgraded to 3.56 or lower and that has installed the official firmware 4.82, without the need of a hardware flasher.

All phat models and the slim models up to 25XX (min ver 3.56 and lower) are supported. Super slim models and slim models 3xxx, 4xxx & 25XX (min ver 3.60 and higher) require ps3xploit v3.0 (HAN). Confirm what model you have before try the exploit!

More info: http://psx-place.com/threads/ps3xploit-now-install-cfw-from-4-82.15500/

Updates to the exploit:
2018-01-24 ps3xploit v2.0 improved exploit for phat & slims models 25xx and lower (only)
2018-03-13 ps3xploit v3.0 (HAN) for super slims and slims 3xxx/4xxx

Tutorial: PS3Xploit Tutorial