I don't use a condom a week before or a week after my period (I don't really enjoy period sex, so I never have it while I'm actively bleeding). I have not gotten pregnant doing this and I've done variations of the rhythm cycle for 10 years.

A woman can ONLY get pregnant if she is ovulating. There is only a small window of time where a woman ovulates. Yes, sperm can live in her body for about a week, but in general, that window only starts about a week after her period ends.

I mean, use a condom if you want. You should DEFINITELY use a condom during fertile periods. You should DEFINITELY use a condom if you don't know your partner well and/or have not had STI testing together. You technically don't have to use a condom when there is almost no possible way she will get pregnant (again, I'm assuming normal, regular cycles here). Crazy things have happened and sometimes women release more than one egg during a cycle, or release the egg early/late but in general, it's fine.

I always get super downvoted when I post this stuff, and of course you should do your own research before just blindly trusting some shmo on the internet, but it's not like a woman will get pregnant every single time a guy cums inside of her. That's just not going to happen. In general, she can't get pregnant while on her period.