Custom firmware was typically achieved through a bugged 1.50 subset and loaded a newer firmware on boot. Later, this method was improved through Pandora and allowed the (then new) slim PSP to run custom firmware too. A breakthrough in "code-signing" lead to the development of a 6.20 custom firmware for PSPgo and PSP 3000. Unfortunately, not all devices these days can use 6.20 firmware.
To solve this, I present 6.61 Infinity. By abusing a bug in 6.31, 6.61 Infinity utilises a similar technique to the old 1.50 firmwares to provide an upto-date custom firmware for all devices, excluding the E1000 (so far). Infinity itself is not a custom firmware; instead it allows the flexibility for users to install any compatible custom firmware they wish. For convenience, Infinity includes built-in functionality for both PRO and ME. Use the Infinity Configurator to update infinity and choose which custom firmware to boot into on start up.
This is my final farewell to the PSP. Bug fixes will be provided, but after 12 years of PSP, this is where it ends for me. I plan to continue work on the vita and start some new, exciting projects. To keep up-to date, follow me on twitter: @DaveeFTW. If you're interested in the technical write-up, check out my blog.
To install, copy PSP directory from the Installer download below to your PSP. Place the 6.31 and 6.61 updates named 631.PBP and 661.PBP respectfully into the MAKER folder. Run the maker application. If successful, there will be a DATA.MFC file in the MAKER folder. Copy this to the FLASHER folder and run the flasher. After this your device will reboot and you'll be in Infinity! From here, install any CFW you wish and activate the permament patch in the Infinity Configuration app.