Both Pentium/Core (and Celeron derivatives of the 64-bit ones) are simultaneously 32 and 64-bit, much like AMD's Athlon64/Opteron, and most Semprons. Hence why, unlike Intel's Itanium's exclusive 64-bit design, these chips did not require one to obtain a 64-bit OS. I'm expanding on the previous response, but basically, he's right. If they're 32-bit, they should run fine. You may run into trouble with 16-bit apps, however, so you may need to make use of compatibility mode.
