In 1996, James McKee was a mathematician departing Trinity Hall, at Cambridge.
Following the tradition of bestowing a farewell gift on the college, McKee devised a prime number with 1350 digits (the college being founded in 1350).
The numbers, when viewed in the configuration below, also depicted the Trinity Hall logo.
Here's the video:
Since it was published, I've seen the following number (I assume prime, I've not checked) which depicts the Hello Internet Nail and Gear logo. It was published on the r/HelloInternet subreddit.
Email me others via numberphile at gmail dot com