Number Spiral Diagonals

Starting with the number $1$ and moving to the right in a clockwise direction a $5$ by $5$ spiral is formed as follows:

21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is $101$ .

What is the sum of the numbers on the diagonals in a $1001$ by $1001$ spiral formed in the same way?

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.