Arrange the digits 1-9 in a 3x3 square using each once only according to the following rules:

- Exactly one prime is directly above a prime two less.

- Each pair of opposite corners sums to the same square total and exactly two columns share another square total.

- Exactly one prime is directly to the left of a non-prime two greater.

- Directly above exactly one square digit is a digit four greater.

- Directly to the right of exactly one cubic digit is a digit one greater.

The required arrangement is as follows:

8..9..7
6..3..5
2..4..1