A great big number proposed by Donald Knuth in his lecture "God and Computer Science", which is part 6 in the "God and Computers" lecture series, which is transcribed in the book Things a Computer Scientist Rarely Talks About.
Using ^ notation, Super K is written as 10^^^^3. That's really quite big (I won't even try explaining how big it is here; go see ^ notation), but it's tiny compared to things like Graham's Number, which is the largest finite number ever to have been used in a proof.
Knuth's point with showing Super K is that "infinity is a red herring", since natural language can't describe the difference between infinity and a large finite number like Super K. The human mind cannot comprehend either, so who, so to speak, is counting? Nevertheless, in Knuth's words (quoting Martin Gardner's comment on Graham's Number), "It's really very small as finite numbers go. Almost all of them are larger than it."
Do not get this confused with Special K, which is a breakfast cereal. It will be your undoing.