MYSQL Row Count Limits?

What is the maximum row count for a table in MYSQL? I have a system with around 600,000,000 rows in three tables. Average Data Length (from data_length column) for these tables is 58,000,000,000 bytes. Upon reaching how many rows should there be an alarm? They are intermittently used so archiving them will involve some additional work. Which of the is advisable? 1. Archiving 2. Moving to big data 3. Leaving them as it is.