Existence of non-context free but decidable languages I've been reading the decidablity and undecidability chapters in Sipser's "Intro to Theory of Computation" however I could not find an explanation on the existence of a language that is both non-context free and decidable. 

The only reference to this was a simple language hierarchy diagram showing where the decidable/recognisable bounds were in relation to language types.

I'm unsure as to how I should approach this but I've thought about proving this by diagonlisation:


Let $M$ be the set of all decideable Turing Machines, and $L$ the set
of all languages that are context-free. (Assume finite alphabet)
By drawing up and filling the table where each language corresponds
to a Turing Machine, I was hoping that I could find a contradiction
in some $m \in M$ where there is no corresponding language $l \in L$.


I know that this will not work as both $M$ and $L$ are countable.

Any ideas on how I should approach this?
You could simply consider the language $L = \{a^k | k \text{ is a prime number }\}$.
This is not a context free language, but surely this is decidable by a Turing Machine that checks if the length N of the input is not divisible by any number between 2 and N-1 .