you can do searching for tweets in google or bing using the following rule (in this example we will try to search for my tweets)
actually there is a plus side if you try to search for tweets in google, you can find many old tweets that dates back to more than 7 days ago starting from now. But if you try to search for tweets using twitter search feature here then you can only search for tweets that are no more than 7 days old, older than that then you can’t find it using the twitter search engine. this is because twitter index get so high so they decided it would be better to index tweets to not more than 7 days old.
anyway please follow my twitter then if you find this information useful. 🙂