Just to be clear, how many prospectors you can have depend on your prospector controller size. A size 1 can only control 1 limpet and the above will be true. A size 3 prospector controller allows two live limpets, meaning if you have one live and fire another, nothing will happen to the first. If you have two live and fire another, the oldest one will fail. A size 5 prospector controller can have 4 live limpets and firing a fifth will cause the oldest one to fail (and give you the "prospector limpet failed" message). A size 7 prospector ... no, there is no reason to go above size 5 ...
For core mining, a size 1 prospector controller is enough. For laser mining, going with at least a size 3 is advisable and you can even go with a size 5 depending on your priorities.
Unlike collector limpet controllers that stop firing once its max number of limpets are out, the prospector limpet controller does not stop you from firing off another one just because it has the max number of limpets out - resulting in limpet failure.