There has been a running myth about cockroaches being able to live forever but that is not true, hence, a myth. Depending on the type of roach species, they could live for a few months to seven years.
Female roaches tend to live longer than males because of their role in reproduction.
In terms of species, the cockroach type with the longest lifespan would be the rhinoceros cockroach. It is documented to have a lifespan of ten years. Among common cockroaches, German cockroaches may have the fastest reproduction rate but they also have the shortest lifespan.