Notable Properties of Specific Numbers
First page . . . Back to page 24
William Williams, Primitive history from the
Creation to Cadmus. (1789). On page 4 we find:
[...] Next, to correct Meto's cycle answerably, [...]
334 years: which 121,991 days exceed by 90 minutes; and 334 tropical
years exceed 4131 lunations just as much.
John Narrien, An historical account of the origin
and progress of astronomy. (1833). In chapter XI, page 232 we find:
[...] from the same authority we learn that Hippaichus had
discovered, by a comparison of eclipses in whnch the moon's anomaly
and latitude were the same, that in 5458 months, or 161,178 days,
there were 5923 restitutions of latitude.
T. J. J. See,
Note on the accuracy of the Gaussian constant of the Solar system,
Astronomische Nachrichten 166 89 (1904).
Kasner and Newman, Mathematics and the
Imagination, (Simon and Schuster, New York) 1940 (also republished in
1989 and in 2001). The story can also be found online search for
Googol plus the leading sentence "Words of wisdom are spoken by
children at least as often as by scientists."
T. Nagell, The diophantine equation x2+7=2n.
Archiv fur Mathematik 4(13) pp. 185-187 (1960). Available from
S. Knapowski, On sign-changes of the difference
π(x) - li x. Acta Arithmetica 7, 107-119
Dmitri Borgmann, "Naming the Numbers", Word Ways:
the Journal of Recreational Linguistics 1 (1), February 1968.
Cover and contents are
and article is
V. E. Hoggat Jr. and C. T. Long,
Divisibility properties of generalized fibonacci polynomials,
Fibonacci Quarterly 113 (1973).
Dennis Ritchie, Fifth Edition UNIX (Bell
(PDP-11 assembler source code for a C library routine), June 1974.
Archive created by The Unix
Heritage Society. (I first found this on a mirror
Nancy Bowers and Pundia Lepi, Kaugel Valley systems of
reckoning, Journal of the Polynesian Society 84 (3), pp.
Ted Bastin et al., On the physical interpretation and
the mathematical structure of the combinatorial hierarchy, Int. J.
Theor. Phys. 18 p. 445 (1979).
David A. Klarner, The Mathematical Gardner,
1980. ISBN 0-534-98015-5
Donald E. Knuth and Allan A. Miller, "A Programming and
Problem-Solving Seminar" (notes from Stanford CS 204, Fall 1980),
pages 4-12. PDF here:
Programming and Problem-Solving Seminar
Carl Sagan, Ann Druyan and Steven Soter (creators),
Cosmos: a Personal Voyage (television series), 1980. Episode 9
has the googol quote.
J. H. Conway and N. J. A. Sloane, Lorentzian forms for
the Leech lattice. Bulletin of the American Mathematical Society
6(2) (March 1982), pp. 215-217.
John Horton Conway and Richard Guy, The Book of
Numbers, New York: Springer-Verlag (1996). ISBN 038797993X.
Wells, David, The Penguin Dictionary of Curious
and Interesting Numbers. (Original edition 1986; revised and
Richard Guy, The strong law of small numbers. The
American Mathematical Monthly 95(8) pp. 697-712 (1988). This has
been used for several university courses and when I last checked was
(also formerly at http://ndikandi.utm.mx/~lm2002070425/Guy.pdf)
The Compact Oxford English Dictionary (Second Edition), 1991.
This is the version that has 21473 pages photographically reduced into
a single book of about 2400 pages.
J. Meeus and D. Savoie,
The history of the tropical year,
Journal of the British Astronomical Association 102(1) pp.
Linda Scele Drawings Collection,
Scele drawing 4087,
Simon et al.,
Numerical expressions for precession formulae and mean elements for the Moon and the planets
James G. Gilson, Calculating the fine structure
constant, 1995. PDF here
Maurice Mignotte and Attila Pethö,
On the system of diophantine equations
x2-6y2=-5 and x=2z2-1. Mathematica Scandinavica
76, pp. 50-60 (1995). Available from the publisher
H. Pierre Noyes. Measurement, accuracy, bit-strings,
Manthey's quaternions, and RRQM. In Entelechies (Proc. ANPA 16),
K. G. Bowden, ed., University of East London. pp. 27-50.
H. Pierre Noyes. Some remarks on discrete physics as
an ultimate dynamical theory.
IEEE Computer Graphics and Applications, 1997.
Richard Crandall, "The Challenge of Large
Numbers", Scientific American no. 276 (Feb. 1997), pp. 74-79.
D. E. Knuth. The Art of Computer Programming. vol 4A.
J. H. E. Cohn, The diophantine system
x2-6y2=-5, x=2z2-1. Mathematica Scandinavica
82, pp. 161-164 (1998). Available from the publisher
Eric Weisstein, The CRC Concise Encyclopedia of
Mathematics (CRC Press), 1998. ISBN 0849396409.
Richard Borcherds, The Leech lattice and other lattices.
Ph.D. thesis, Trinity College (originally given June 1984), as corrected
Georges Ifrah, The Universal History of Numbers, ISBN
Problem of the month (August 2000), web page, 2000-2009.
What's Special About This Number?, web page, 2000-2009.
The Fano Plane
(web page) 2001. (Part of a collection describing the Octonions)
Palais, Robert. "π Is Wrong!". The Mathematical
Intelligencer 23 (3) 7–8 (2001).
Fast inverse square root,
2002 (as archived on 2003 Apr 26 by the Internet Archive Wayback
Michael Janssen, The Trouton experiment and E=mc2 (handout, PDF
A new precession formula.
Public Relations Center,
Chris Lomont, Fast inverse square root, 2003.
23 Oct 2003.
2003. Available from arxiv.org.
M. Agrawal et al., PRIMES is in P. Annals of
Mathematics 160(2) pp. 781-793 (2004). Available from the
Dario Alpern, Known 3-digit prime factors of
Googolplexplex - 1, web site, 2004.
Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe, 2004.
Maohua Le, On the diophantine system
x2-Dy2=1-D AND x=2z2-1. Mathematica Scandinavica
95, pp. 171-180 (2004). Available from the publisher
Gordon, Raymond G., Jr. (ed.), Ethnologue:
Languages of the World (15th edition), SIL International, Dallas
(2005). Online version at
Clifford Pickover. A Passion for Mathematics:
numbers, puzzles, madness, religion, and the quest for reality.
Wiley (2005). ISBN 0-471-69098-8.
Klein's Quartic Curve
(web page) July 28, 2006.
Bailey, Borwein, Kapoor and Weisstein,
Ten Problems in Experimental Mathematics, American Mathematical Monthly, 2006.
Andrew Granville and Greg Martin, Prime number
races, The American Mathematical Monthly 113(1) pp. 1-33
(2006). Available from the AMM
a 2004 preprint is on arxiv.org.
Don N. Page, Susskind's challenge to the Hartle-Hawking
no-boundary proposal and possible resolutions, 2006.
Mark Ronan, Symmetry and the Monster: The Story of
One of the Greatest Quests of Mathematics, 2006. ISBN 0-19-280723-4
Alan H. Guth,
Eternal inflation and its implications,
2nd International Conference on Quantum Theories and
Renormalization Group in Gravity and Cosmology (IRGAC2006),
Barcelona, Spain, 11-15 July 2006.
David de Neufville, personal correspondence.
My Favorite Numbers (web
page) 2008. Includes videos and slides from three talks given in 2008
at University of Glasgow.
Andrew Granville, Prime number patterns, The
American Mathematical Monthly 115(4) pp. 279-296 (2008). Available
from the MAA
and from the author
My Math Forum, discussion thread,
2008 Oct 10
N. J. A. Sloane,
Eight Hateful Sequences, 2008.
Ken Auletta, Googled : the end of the world as we
know it (New York : Penguin Press, 2009) ISBN 9781594202353.
Daan van Berkel, On a curious property of 3435. (2009)
CNN Beat 360, Anderson Cooper Daily Podcast for July
Man Charged 23 Quadrillion...,
July 15th, 2009.
Andrei Linde and Vitaly Vanchurin, How many universes
are in the multiverse?, 2009.
WMUR TV-9 (Manchester NH),
Man's Debit Card Charged $23 Quadrillion...,
July 15th, 2009.
Card Users Hit With $23 Quadrillion Charge,
July 15th, 2009.
Fast inverse square root (revisited), 2010.
Jeffrey Hankins, personal correspondence, 2010.
Theodore P. Hill, Ronald F. Fox, Jack Miller,
A Better Definition of the Kilogram
(note on page 5: "At this point in time, it is not yet possible
to obtain exact counts of individual atoms, even when they are in a
crystal lattice, but that is merely a question of time.")
David Stuart, Notes on Accession Dates in the
Inscriptions of Coba, 2010. Available
Mark R. Diamond,
Multiplicative persistence base 10: some new null results, 2011.
Nicolas Gauvit et al.,
Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?,
Ivan Panchenko, personal correspondence, 2011.
The Skewes number for twin primes:
counting sign changes of π2(x) − C2Li2(x),
2011. Available from arxiv.org.
"fp Plugin 5.1",
message to realbasic-nug forum (mirror
30 Jan 2012
(blog article), 2012.
The Lucas-Lehmer-test for Mersenne-numbers and the number Λ ~1.389910663524...,
April 4 2012.
xkcd 1047 -- Approximations (online
comic strip), April 25 2012.
Note : This strip mentions my ries program because
Munroe used it to derive some of the expressions, near-equalities
and approximations shown in the strip. He and I did not communicate
prior to the publication of the strip, and all of the material in the
strip was found by him. Answering a presumably large volume of
responses, he specifically commented on this fact in a note at the top
of the comic (which was visible for a while on the first day) by
"Note: '1 year = π × 107 seconds' is popular with
physicists. For this list, I've tried to stick to approximations that
I noticed on my own."
There are a few obvious exceptions which were included for their
amusement value: the Rent approximation
525600×60 ≈ 31556952, and
1/140 as an approximation to the reciprocal of the
fine-structure constant (the comment "I've had
enough of this 137 crap" refers to the fanatical
cult of 137).
Robert Munafo, answer to
a question by Mahmud.
The relevant discussion is also here:
What happens when numbers become large... really large?
"The Origin of Life -- Evolution's Dilemma (web page), accessed 2010 April 29.
"computational knowledge engine" online resource.
27: This is close.
Quick index: if you're looking for a specific number, start with
whichever of these is closest:
Also, check out my large numbers
and integer sequences pages.