I just posted about this in the June ddc, but I'll mention it here, too. :) I begin getting BH at 11 weeks each pregnancy. They continue to come just a little more often and just a little bit stronger throughout my pregnancies until the last month or 2 when I am a BH party queen. Or something.
Just think of them as exercise for your uterus! They are preparing your uterus for all the work it will do on the Big Day.
Snozzberry, obviously I'm not a doctor so feel free to ignore me, but my personal experience has been that I very frequently (especially during the 3rd trimester, but sometimes earlier as well) have BH far more than 4 per hour. Especially if I need to empty my bladder, am wearing a seat belt, or am wearing clothes that are even slightly constricting to my lower belly. I dreaded all my appts back in the day during the 2nd half of my pregnancies when I was seeing traditional OBs and doctor folks because they would freak out about my BHs. Many times during my 2nd and 3rd pregnancies I would be strapped into a hospital bed and monitored. They'd find me having BH regularly, freak out, give me anti-labor meds, and put me on bed rest! (I was on bed rest my first 2 pregnancies! And probably was for my 3rd but by then I stopped listening. LOL)
The point to all my blabber is that for some women, having very frequent BH is really, really normal and doesn't mean that you're at risk for early birth. Although my 1st baby was born prematurely, she was extremely ill & needed surgery. I don't believe her early birth had anything to do with my BH. I contracted just as much in subsequent pregnancies & all were born within days of my being 40 weeks, with zero signs of preterm labor (besides the BH around the clock, that is LOL). And I got bold enough to just announce to my midwives that I contract like a crazy contractor person and please just try to ignore them. :)
If you notice any other signs of labor, that is when I would personally pay closer attention to all those BH. Like blood, fluid, the contractions becoming stronger, etc. So, my personal answer is that no, you shouldn't be worried a bit. Just go about life as usual and only worry if you notice any other weird signs.