I thought of this out of the blue and I don't want to take the time to research it but here's the question: Beginning in 1901, which is considered to be the first year of the modern era of baseball, what is the shortest overlapping chain of players who played in the majors? By overlapping I mean players would have to play in the same year to be part of the chain. To illustrate what I mean, here's the hypothetical scenario. Say there was a player who played every year from 1901 through 1921, another who played 1921-1941, another who played 1941-1961, another who played 1961-1981, another who played 1981-2001, and another who played 2001-2018. That would be a chain of 6 players. I suppose a good place to start would be to find players who had very long careers. For example, Jim Kaat comes to mind (25 years).