Prosperity means to thrive. It means to have the appropriate abundance necessary to maintain life and where appropriate grow.
Currently there are many different definitions of sustainability. Most of these definitions contain elements for not only allowing life to survive, but more importantly allowing life to thrive in all the important and meaningful ways --- for longer and longer periods of time.
"When its new definition and opportunities are understood, the new ideas of sustainability prosperity are indispensable for both long term financial viability and short term prosperity." Lawrence Wollersheim