I've heard the same thing. I've heard it's not uncommon for first-time moms to go completely up to the 40 weeks or sometimes even after. And then second time moms have heard that it's not uncommon for them to be giving birth around week 38 and 39 instead of like 40 41
Well My first my water leaked at 36 wks 6 days, amd had her exactly at 37 weeks. My second I had a irratable uterus at 34 weeks, and went into real labor at 35 weeks.
My third I started contracting at 37 weeks, and two days later I had him.
I am now 34 weeks 3 days, and all I have is bracton hicks. Also I feel like my pelvoc bone is getting ripped apart. 😑