==> pickover/pickover.11.p <==
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, e-mail 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.