Usenet Newsgroups : rec.puzzles Hall of FameThe rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided. Many of these puzzles also appear in Braingle's own collection. 

Title: Cliff Puzzle 11: The Leviathan Number From: cliff@watson.ibm.com If you respond to this puzzle, if possible please send me your name, address, affiliation, email address, so I can properly credit you if you provide unique information. PLEASE ALSO directly mail me a copy of your response in addition to any responding you do in the newsgroup. I will assume it is OK to describe your answer in any article or publication I may write in the future, with attribution to you, unless you state otherwise. Thanks, Cliff Pickover * * * Many interesting observations have recently been published concerning various number theory properties of the "number of the beast", 666. In this new puzzle here I ask you to consider the monstrous "leviathan number", a number so large as to make the number of electrons, protons, and neutrons in the universe (10**79) pale in comparison. (It also makes a googol (10**100) look kind of small). The leviathan number is defined as (10**666)!, where the "!" indicates factorial. 1. What are the first 6 digits of the leviathan number? Hint: you need not actually compute the leviathan to determine this. If you can determine the first 6 digits, please carefully spell out your method. 2. Could modern supercomputers compute the leviathan, or will this beyond the realm of humankind for the next century? 3. Even if we cannot compute the leviathan, how many other characteristics of this number can we write down.
Solution