I remember Jeff Atwood (@codinghorror) had posted a tweet about a new website, but I can't seem to find the link.
Is there any way I can search within someone's tweets to find that link?
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Remy Sharp wrote a website application that will search your, or someone else's tweets without the limitations Twitter imposes so you can search far further back in time. It's at http://snapbird.org/.
Twitter has an advanced search form that you can use.
Also note that Twitter does not retain an infinitely long history of messages, you may not be able to find a Twitter message from the past.
Twitter’s advanced search isn’t available on the mobile app. If you’d like to search by date on the mobile app you can still do so the old-fashioned way using the “since:” and “until:” operators.
In addition to all your asnwers up there, there's another great search for old tweets. Click on Backtweets, it works perfect.
If you can remember what the site was about or a word or two from the tweet, twitter has an advanced search which allows you to specify a user's tweets to search
I have got better results with https://queryfeed.net/ more relevant results although the website does have a downtime at times.