Answer to the question:
Assume you’re in the tender process and preparing your financial proposal or estimating the cost of the project, there are always some items (equipment, material,…) that you are not sure about their cost.
You also may find that there is a part of the scope of work still not clear or its data isn’t ready yet, so you price it according to an estimation.
The price of the items (equipment, material,…) which you know clearly everything about it, but you can’t use its current price or you don’t even know it’s current price, that’s what is called Prime cost.
While the Provisional sum is the cost that you put for the unknown scope of work that you don’t know anything about it.
They’re both estimated cost for something we don’t know, but the prime cost is usually called for the activities or material that you know it but not certain about its price.