The discussion centers on identifying the variable star with the longest period, with an initial focus on Mira variables. While Mira variables typically have periods up to 700 or 1000 days, a source mentions a star with a period of 1630 days. Epsilon Aurigae is noted as a long-period pulsating variable, though it is not a Mira. The conversation highlights the challenges of studying very long period variables, particularly those in the infrared range. Overall, the quest for the longest period variable star continues, emphasizing the complexity of these celestial phenomena.