I've never before heard of 3.51 OFW for PS4 a Slim console I have however heard of instances where certain different variations of OFW revisions on the system. usually, the hackable FW is 3.55, so you should be good though, there was recently a display on twitter for a debug menu settings on 3.55 whatever you do don't update past 3.51, there.
Programmers will likely need to find out the best they can about that FW given the chance they haven't and yes there's a browser hack. but it's mostly for research atm because of things not being publicly announced.
In other words, the full exploit is not public, but there's a part of it, and you'll be able to o find it HERE.
Just navigate there on the PS4 browser also try the 4.0x PS4 Entry Point. Should work.
I just purchased a new PS4 slim and it came with version 3.51 software. Should I leave it on 3.51 or upgrade to a newer version? If so what would you suggest for a version? I don't want to lock myself out of any CFW or jailbreaking.