Logic Masters Deutschland e.V.

This puzzle has been my tenth feature on Cracking the Cryptic (click here to see Mark solving it). It has been created in honor of Phistomefel, where my goal was to use the Phistomefel ring in a completely different way than usual. Be aware that the mid-solve is (at least in my opinion) quite challenging, which is the main reason for my initial rating of 4-star difficulty. I hope that you enjoy the puzzle. Constructive feedback is always appreciated! The rules are as follows:

Normal sudoku rules apply. Digits are not allowed to repeat on any positive diagonal (i.e. any diagonal going from the lower-left part of the grid to the upper-right part of the grid). A digit x in a black circle indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally and diagonally adjacent cells) contain a digit that is in a 1:2 ratio with x. All black circles are given. The sum of the digits in Phistomefel's ring (marked by the cage) is prime.

You can play this puzzle via the following link: https://sudokupad.app/wbwn6dl8xz