Cheryl's Sandwich Sudoku

https://git.io/JtcZS

Cheryl has set a sandwich sudoku for Albert and Bernard with the following ruleset:

-- Normal 6x6 sudoku rules apply: Every row, column, and 2x3 regions contain digits 1-6.
--  Sandwich rule applies: Digits outside the grid describes the sum of the digits between 1 and 6 (called the “crusts”), excluding the crusts. This sum is called the “sandwich sum”.
-- R4C4 must be larger than R4C5. This is marked by the inequality sign.

Albert is only given the row clues and Bernard is only given the column clues. They have the following conversation:

Albert: I know whether R1C3 is a crust.
Bernard: I know where the crusts in column 1 are.
Albert: I didn’t know where the crusts in row 1 are, but now I know. I also know R6C2 is not a crust.
Bernard: I already knew R6C2 is not a crust.
Albert: I don’t know how far apart the crusts are in row 2, but I know whether R2C4 is a crust.
Bernard: I already knew how far apart the crusts are in column 4, but I still don’t know where they are. In addition, I know whether R4C3 is a crust, but I don’t know whether the other cells are a crust.
Albert: I still don’t know where the other crust in row 6 is.
Bernard: I didn’t know how far apart the crusts are in column 6, but now I know.
Albert: None of my clues are 0.
Bernard: The sandwich sum in column 4 is a prime number.
Albert: The sandwich sum in row 3 is not a prime number.
Bernard: The sandwich sum in column 5 is a prime number.
Albert: I know the solution to this sudoku.
Bernard: I know the solution to this sudoku.