Nintendo says Prime 4 is the start of a new story, and the Prime Trilogy ended its arc with Prime 3.

https://www.nintendo.com/jp/topics/article/ed98179e-b57e-4ae8-8ac5-3cdc5d721661

This is something that has been known by longtime fans, and reaffirmed by the series producer in 2015, but in case newcomers weren't aware, it's totally fine to not have played Prime 1-3 before starting 4.