The term 'A Rapid Increase in Number' can be summarized by three crossword solutions: Proliferation (13 letters), UPSURGE (7 letters), and HOTBED (6 letters). Proliferation refers to a rapid increase in the number of something, usually over a short period of time. An UPSURGE is a sudden, sharp increase in something, such as activity or intensity. A HOTBED is an environment that encourages the rapid growth or development of something. All three words refer to a rapid increase in number, but each has its own nuances.