A traveller decided to explore a square desert. He started from a point on the edge to point B, travelling perpendicular to the edge of the desert he started on. On reaching B, he then decided to take a 90 degree turn to travel to point C, where he spent the night.
The next day he was told that he could go straight and reach point D, take a 90 degree turn towards the starting point turn and reach point F (which were both on the edge of the desert), or go to a A which was further interior in the desert - which would require him to travel at an unknown angle. He chose to travel to A.
After spending another night at A, He retreated to his original starting point by day end. Though he did not intend to, he passed through point B before reaching his final destination.
He was then amazed to find that he had travelled the same distance in the last two days, and the distance covered by each of those two day's travels was a whole prime number.
He also concluded the following from his records
The distances he had travelled from A to B and from B to C added up to the next prime number (to the prime number he estimated to have travelled in each of the last two days)
When he decided to retreat he was equally far from all the corners of the desert
All his travels were in perfect straight lines, the only turns he took where when he travelled from point B to C and C to A and A to his starting point.
He noticed that the distance he travelled from A to B was significantly shorter than his travel from B to C
He was wondering if he could find out how far he was from D and F when he decided to travel to A - can you help him?
As you may have realised by now, I made this up, so if you think I am missing something add in comments.
Edit: There are two possible values after my last edit and one of them is captured, but not the other, so I have accepted the answer with one of them now, but will upvote anyone coming up with both