well vishal I was kidding with that answer. I know that i stands for Itanium as "linkgx1" has already mentioned. Itanium is a 64 bit architecture which intel developed and it serves as the backbone of the corei series. Itanium was jointly developed by intel and hp.
From my understanding, core architecture and Itanium architecture have both been used for Intel's current corei series.
whether core itself is a derivative of Itanium is something I do not know.
Numbers 3, 5 and 7 were choosen for simplicity for clear demarcation of intels, Budget (i3), mainstream(i5) and high end parts (i7). why exactly this number set was chosen is not clearly explained though I speculate that after core solo and core2 only remaining singe digit prime numbers were 3,5 and 7. just my theory