Nice recursive solution. I didn't think of this solution. It took me some time to understand what the creator of the Kata meant. The description was kinda vague.

It is a good solution. I would suggest that you do: input.ToLower() .ToCharArray() .ToList() etc. Then you have more readable code. If you look at my solution you see how it can be achieved without using the dictionary. But it is still a good solution :-)

A small hint:
Primes.GetInBound() returns a List now, but since nobody is going to (and should not) modify the list, it you could convert the list to an array and let the function return long[]. That locks down the list against accidental modification.

Nice idea to make IsPrime an extension of long!

Nice collection of gears, nuts and bolts! :)

Thanks. I like your implementation of extension methods. Makes a lot of sense and allows a first-to-last method call notation rather than the last-to-first one I am forced to use.

Your solution looks almost as mine only i would recommend to implement the transformations as extensions :) looks more clean. For the rest good job!

Charming combination of a very readable top level function, cleanly separated responsibilities and a recursion algorithm!

One small improvement could be to make the sequence a distinct sequence, before feeding it in the foreach loop. That way, you wouldn't be trying the same numbers multiple times.

foreach (var integer in sequence.Distinct())

It's a less elegant attempt at what you do with the Hits and BattleOutcomes. Glad to see my implementation does have a context-specific advantage.

Fun idea, to have the powerBalance in there.
Let it emit some events and you can create a GUI on top of it that plays out the battle visually ;-)