If you are referring to running the current version of Premier Elements i.e. 14.1 I am editing HD videos with an i3-4130 CPU @ 2.40 GHz (Win 7 64.bit) and it whilst I can work with it the preview (even when rendered) can have a rather jerky appearance. The resuting video (eg on Blu-Ray or MP4) is fine.
I am considering upgradung my CPU.
Bottom line: depending on what you are doing (eg what type of videos you are working with) i3 may be just sufficient or may not be.
Correction to typo above - Iits should read 3.40 GHz instead of 2.40!!!
Using the benchmark chart, I've found you can get decent performance with a rating of a 3000 or more and very good performance with 5500 or more. So it kind of depends on which i3 you have. (Hotelechomike's processor rates a 4700.)
It also matters what video you're editing. Standard definition and AVCHD should edit pretty efficiently on a decently powered machine. 4K and 1080p would likely need a more powerful processor.
Yes program will probably run on a i3 but...........
Also it depends largly on what kind of footage you are going to edit.
SD (mini-dv) footage wont be a problem. AVCHD is going to be a big problem. Latter is cpu intensive.
You can always download the trial and have a go at it.
It very important a computer is well configured.
At least two separate internal 7200 hdd's; one for OS and program's and one for the rest.