There are an infinite number of solutions for the constraint for a single base. When you consider the probability of a solution occurring amongst the set of num

There are an infinite number of solutions for the constraint for a single base. When you consider the probability of a solution occurring amongst the set of numbers of equal length, it becomes apparent that the size of each set grows faster than the number of solutions it contains. Requiring the number to satisfy the constraint for multiple bases causes the probability to decrease rapidly. This naive heuristic analysis suggests that the probability of finding a solution is not only inversely proportional to the chosen base, but also inversely proportional to the value of the chosen candidate.