Logic Masters Deutschland e.V.

A puzzle about prime numbers! You can find the puzzle on F-Puzzles and Cracking the Cryptic. Have fun!

Rules:
-Normal sudoku rules apply (place the digits 1-9 in every row, column, and box).
-In the cages, multiplying the first and second number yields the number after the '=' sign. These multiplication totals are strictly decreasing from top to bottom (e.g., the number after the '=' sign on row 2 is larger than the number after the '=' sign on row 4).
-On every blue line, taking only the prime numbers (2,3,5 and 7) and ignoring the other numbers, the numbers are strictly decreasing from the top left to the bottom right. Every blue line contains at least one prime number.
-Cells with a square contain prime numbers that indicate the size of an orthogonally connected area of prime numbers, surrounded orthogonally by non-prime numbers.
-Cells with a circle contain a number (not necessarily prime) that indicates how many cells directly around it (orthogonally and/or diagonally, including itself) contain a prime number.
-Not all circles, squares and blue lines are given.

Please leave a comment with feedback so I can learn how to make better puzzles!

Example of the circle rule: Example of the square rule: Example of the line rule: