Euler project: Ulam spiral

Spiral like this:

This spiral is famous because it has the fact that most of prime number are present on the diagonal position of this rectangular.

Euler problem ask for the sum of all diagonal numbers like red ones above. The prime feature could not be used because not all diagonal positions are prime number. The hint is just every turn in this spiral, the length goes like: 1, 1, 2, 2, 3, 3, 4, 4,...

Since every turn is also the diagonal, except the first one, 2, use this length growth to build the sum is easy:

Every first odd turn should be taken care of because the actual diagonal number is the one before the turn number. Also, note the last turn is not included to form the required rectangular.