Conversation so far:
when is a decision problem said to be polynomially reversible
The Boolean satisfiability problem is complete for the class NP of decision problems under polynomial-time reducibility.
How is a decision problem used to determine a prime number?
It is possible to effectively decide whether a given natural number is prime by testing every possible nontrivial factor.
How is a decision problem used to determine whether a number is divisible?
The answer is either 'yes' or 'no' depending upon the values of x and y.
When is a decision problem said to be difficult?
Difficult in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem.

Question: When is a problem decidable?
Self-contained rewrite: When is a decision problem said to be decidable?