According to this page:
the following Intel CPU's are 64bit:
Intel F and 5x1 series Pentium 4 using the "Prescott" core Pentium D Core 2 (Solo, Duo & Quad) Core i5 (all) Core i7 (all)
Isn't the Core i3 64 bit too?
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They must have left it out. It is 64 bit, there is the Intel 64 support which is an x86-64 extension like AMD64. http://en.wikipedia.org/wiki/List_of_Intel_Core_i3_microprocessors
All Intel Core i3 Processors (Sandy Bridge and Clarkdale ) are 64x architecture. Even though Clarkdale is based off of Westmere architecture, they use 64 bit architecture. I'm willing to bet this is a typo or something, considering the entire "i" generation was meant for 64 bit architecture to meet the expanding needs to computers RAM requirements, laptops incorporated graphics (internal GPU) and, higher processing/ thread count.
Another option to determine if your processor is 64-bit is to look up at http://ark.intel.com/.
If it says „64-bit”, you've got a 64-bit processor.