Go forth and multiply (Variant Sudoku)

[Nightmare2805]

I would like to recommend my own puzzle. https://logic-masters.de/Raetselportal/R...?id=000EBL

Normal Sudoku rules apply.
On arrows digits must multiply to the number in the arrows circle.
On thermos digits must multiply from the bulb end. (i.e. every digit along the thermo must be a multiple of the previous digit.)
Digits in a cage cannot repeat and cannot sum to a prime number.
Purple lines must be split into 2 segments with digits that multiply to consecutive numbers.
Digits may repeat on a purple line if allowed by other rules.
A segment of a purple line can be of any length.

I hope you enjoy it.