The intuition is to employ a depth-first search (DFS) approach through the tree.
During each step in the traversal, we perform the following key calculations:
1. Determine the path that ends at the current node.
2. Compute two different subtree paths that traverse the current node.
3. Maintain an array that keeps track of the cases where paths contain either 0 or 1 prime number.
This method allows us to efficiently count the valid paths in the tree while considering the presence of prime numbers.