I have a website with many images embedded within articles. I do not want to miss traffic by image search. It is easier to save images with numbers, but will this affect SEO rank? I mean image search engines mainly pay attention to the file name or img alt (or title) and text around the image?
You absolutely want to name your images with informative names as @paulmorriss said. One reason is that Google doesn't place much if any importance in the img alt tag because of how easy it is to stuff for SEO purposes.
Another thing you can do to help SEO is create an image sitemap. http://www.google.com/support/webmasters/bin/answer.py?answer=178636
Yes, it will.
Give your images detailed, informative filenames