4D Prince of Persia is an unofficial fan-made copy of the original Prince of Persia for MS-DOS made by a developer labelled only as Terebilov K.A.
Now you may be asking why you should care when the original Prince of Persia is already on the dreamlist. There a couple of reasons that are as follows:
1. The Gaming History. 4D Prince of Persia was actually more prevalent (more readily available) than the original Prince of Persia and this unofficial copy was actually played by more people than the original. Countless people told stories of playing what they believed to be the official Prince of Persia, before being informed that what they had actually played was a fan-made copy that had fooled them into believing it was the official game.
2. The Quality. This unofficial copy of Prince of Persia is extremely good, to the degree that it caused mass confusion over what was actually the original Prince of Persia at the time (see the point above). While most of the graphical assets were likely ported over, a number of coding changes had happened underneath to alter various parts of the game and unlike most fan-projects at the time, this one was very stable and very polished.
3. The Difficulty. 4D prince of Persia is more akin in difficulty to what could be considered a modern romhack, where the original assets of a game are adjusted and reogranised to increase the challenge for players who find the original games too easy. In this case the levels have been redesigned to be harder to navigate and with greater verticality making them far more hazardous to the player, while the enemies have been recoded to make combat with them more challenging and cause them to pose a greater threat.
Why this should be on GOG though (if the original Prince of Persia ever arrives) is the fact that this can be seen as essentially a New Game+, a final challenge for those players who have completed the original game as Prince of Persia's replayability is limited by it's linear path.