I am trying to model the spread of information on Twitter, so I need the number of tweets with specific hashtags and the time each tweet was posted. If possible I would also like to restrict the time period for which I am searching. So if I were examining tweets with the hashtag #ABC, I would like to know that there were 1,400 tweets from 01/01/2015 - 01/08/2015, and then the specific time for each tweet. I don't the actual tweet itself though. From what I've read so far, it looks like the Twitter API restricts the total number of tweets you can pull and limits how far back I can search. Anyone know if there's a way for me to get this data?
Twitter api provides historical data for a hashtag only up to past 10 days. There is no limit on number of tweets but they have put limitation on time.
There is no way to get historical data related to a hashtag past 10 days except:

You have access to their premium api (Twitter has recently launched its premium api where you get access only if you qualify their criteria. Till date they have provided access to very limited users)
You can purchase the data from data providers like Gnip
You have internal contacts in Twitter ;)
How can I get the number of tweets associated with a certain hashtag, and the timestamp of those tweets?