What is the classification of a slender, tightly coiled, or corkscrew-shaped bacterium that can wriggle about?

The classification of a slender, tightly coiled, or corkscrew-shaped bacterium that can wriggle about is categorized as a spirochete. Spirochetes are a specific group of bacteria characterized by their unique spiral shape and flexibility, allowing them to move in a corkscrew motion. This movement is facilitated by their internal flagella, which help them navigate through viscous environments.

In contrast, cocci are spherical bacteria, bacilli are rod-shaped, and spirilla are also spiral-shaped but tend to have a more rigid structure compared to spirochetes. Therefore, while different types of bacteria can exhibit spiral shapes, the description provided distinctly aligns with the characteristics of spirochetes, making it the correct classification.