Clustering is a fundamental primitive in manifold applications. In order to achieve valuable results, parameters of the clustering algorithm, e.g., the number of clusters, have to be set appropriately, which is a tremendous pitfall. To this end, analysts rely on their domain knowledge in order to define parameter search spaces. While experienced analysts may be able to define a small search space, especially novice analysts often define rather large search spaces due to the lack of in-depth domain knowledge. These search spaces can be explored in different ways by estimation methods for the number of clusters. In the worst case, estimation methods perform an exhaustive search in the given search space, which leads to infeasible runtimes for large datasets and large search spaces. We propose LOG-Means, which is able to overcome these issues of existing methods. We show that LOG-Means provides estimates in sublinear time regarding the defined search space, thus being a strong fit for large datasets and large search spaces. In our comprehensive evaluation on an Apache Spark cluster, we compare LOG-Means to 13 existing estimation methods. The evaluation shows that LOG-Means significantly outperforms these methods in terms of runtime and accuracy. To the best of our knowledge, this is the most systematic comparison on large datasets and search spaces as of today.