The maximum number of tweets you can return per page is 100. If you return all the pages available you can get to around 1,500 max. These limits are defined in the search API documentation. (
http://dev.twitter.com/doc/get/search).
You may be better either looking at the streaming API and hope some of the Tweets you are looking for turn up, or use your random number generator to search "n" times and pull back 100 Tweets at a go. You would have to set an interval between searches otherwise you are likley to pull back the same Tweet more than once, especially if it is a seldom used hashtag.
Perhaps if you have a number of hashtags you are looking for, you could "round robin" through all of them with a suitable delay between each one (still checking for duplicates)... or possibly check for the same hashtag at the same time each day if you are looking for some sort of frequency indicator. Alternatively add some sort of randomness to the date range per your example.
Paul