Does it make sense to back pay 6 (fully exempt) months of missing pension contributions?

Hi, before starting my full-time job some years ago I was an intern. While I could have paid into the basic pension back then, I didn't think that I would be staying in Japan after the internship, so I went to the pension office and they exempted me from paying due to being a student at that time.

I am pretty certain that I will stay in Japan long-term, or at least long enough to reach the 10 year minimum pension contributions.

Does it make financial sense to back pay those 6 month to increase the monthly pension payments later?
If yes, can I do it online, or I would have to go to the pension office? Nenkin-net gives me an error when I try clicking on those exempt months.

by Iekei_ramen