> There is no such thing as an Intel Core* CPU that is 32bit. Actually, the first "Core" branded CPUs ("Core Solo" and "Core Duo") were still 32bit, back in 2006 (that was the time-window during which AMD had already switched to 64bit CPUs and Intel still hoped it could move people over to IA64 instead).
The Core 2 line that followed soon after (around 2006-2007) introduced the amd64 architecture to the "Core" brand. Stefan