According to this page:
https://help.ubuntu.com/community/32bit_and_64bit
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?