Notable Properties of Specific Numbers
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Bibliography
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[...] 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.
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[155] 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.
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[162] 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. PDF here
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[165] Jim Blinn, Floating-point tricks, IEEE Computer Graphics and Applications, 1997.
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[170] Richard Borcherds, The Leech lattice and other lattices. Ph.D. thesis, Trinity College (originally given June 1984), as corrected in 1999.
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[173] Erich Friedman, Problem of the month (August 2000), web page, 2000-2009.
[174] Erich Friedman, What's Special About This Number?, web page, 2000-2009.
[175] Masanobu Kaneko, [The Akiyama-Tanigawa algorithm for Bernoulli numbers, Journal of Integer Sequences 3 00.2.9 (2000).
[176] John Baez, The Fano Plane (web page) 2001. (Part of a collection describing the Octonions)
[177] Palais, Robert. "π Is Wrong!". The Mathematical Intelligencer 23 (3) 7–8 (2001).
[178] David Eberly, Fast inverse square root, 2002 (as archived on 2003 Apr 26 by the Internet Archive Wayback Machine).
[179] Michael Janssen, The Trouton experiment and E=mc2 (handout, PDF file), 2002.
[180] Eric Balandraud, Calculating the Permutations of 4D Magic Cubes, 2003.
[181] Toshio Fukushima, A new precession formula. Public Relations Center, NAOJ, 2003.
[182] Chris Lomont, Fast inverse square root, 2003.
[183] Byron Schmuland, "Shouting Factorials!", 23 Oct 2003.
[184] Max Tegmark, Parallel Universes, 2003. Available from arxiv.org.
[185] M. Agrawal et al., PRIMES is in P. Annals of Mathematics 160(2) pp. 781-793 (2004). Available from the editors here.
[186] Dario Alpern, Known 3-digit prime factors of Googolplexplex - 1, web site, 2004. http://www.alpertron.com.ar/glpxm1.pl?digits=3
[187] Sean M. Carroll and Jennifer Chen, Spontaneous Inflation and the Origin of the Arrow of Time, PDF on arXiv
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[189] 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 here.
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[192] http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf Charles H. Lineweaver and Tamara M. Davis, Misconceptions about the Big Bang, Scientific American, February 2005.
[193] Clifford Pickover. A Passion for Mathematics: numbers, puzzles, madness, religion, and the quest for reality. Wiley (2005). ISBN 0-471-69098-8.
[194] John Baez, Klein's Quartic Curve (web page) July 28, 2006.
[195] Bailey, Borwein, Kapoor and Weisstein, Ten Problems in Experimental Mathematics, American Mathematical Monthly, 2006.
[196] Andrew Granville and Greg Martin, Prime number races, The American Mathematical Monthly 113(1) pp. 1-33 (2006). Available from the AMM here; a 2004 preprint is on arxiv.org.
[197] Don N. Page, Susskind's challenge to the Hartle-Hawking no-boundary proposal and possible resolutions, 2006. arXiv:hep-th/0610199v2
[198] Mark Ronan, Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, 2006. ISBN 0-19-280723-4
[199] 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.
[200] David de Neufville, personal correspondence.
[201] John Baez, My Favorite Numbers (web page) 2008. Includes videos and slides from three talks given in 2008 at University of Glasgow.
[202] Andrew Granville, Prime number patterns, The American Mathematical Monthly 115(4) pp. 279-296 (2008). Available from the MAA here and from the author here.
[203] My Math Forum, discussion thread, 2008 Oct 10 (formerly at www.mymathforum.com/viewtopic.php?f=38&t=4629&start=0) containg a translated description of what the number means:
Given one walking in an axis randomly, each step he goes forward by π or backward by 1 with same probability, the probability that he will return back is it.
[204] N. J. A. Sloane, Eight Hateful Sequences, 2008.
[205] Ken Auletta, Googled : the end of the world as we know it (New York : Penguin Press, 2009) ISBN 9781594202353.
[206] Daan van Berkel, On a curious property of 3435. (2009) arXiv:0911.3038
[207] CNN Beat 360, Anderson Cooper Daily Podcast for July 15th, 2009.
[208] Huffington Post, Man Charged 23 Quadrillion..., July 15th, 2009.
[209] Andrei Linde and Vitaly Vanchurin, How many universes are in the multiverse?, 2009. arXiv:0910.1589v2
[210] WMUR TV-9 (Manchester NH), Man's Debit Card Charged $23 Quadrillion..., July 15th, 2009.
[211] http://www.astro.ucla.edu/~wright/cosmology_faq.html Edward L. Wright, Frequently Asked Questions in Cosmology (web page), 2009.
[212] WTOV, Card Users Hit With $23 Quadrillion Charge, July 15th, 2009.
[213] David Eberly, Fast inverse square root (revisited), 2010.
[214] Jeffrey Hankins, personal correspondence, 2010.
[215] 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.")
[216] David Stuart, Notes on Accession Dates in the Inscriptions of Coba, 2010. Available here.
[217] Mark R. Diamond, Multiplicative persistence base 10: some new null results, 2011.
[218] Nicolas Gauvit et al., Sloane's Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?, 2011.
[219] Ivan Panchenko, personal correspondence, 2011.
[220] Marek Wolf, The "Skewes' number" for twin primes: counting sign changes of π2(x) − C2Li2(x), 2011. Available from arxiv.org.
[221] Bob Delaney, "fp Plugin 5.1", message to realbasic-nug forum (mirror here), 30 Jan 2012
[222] Adam Goucher, Lunisolar calendars (blog article), 2012.
[223] Gottfried Helms, The Lucas-Lehmer-test for Mersenne-numbers and the number Λ ~1.389910663524..., April 4 2012.
[224] Randall Munroe, 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 stating:
"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).
[225] Robert Munafo, answer to a question by Mahmud. The relevant discussion is also here: What happens when numbers become large... really large?
[226] "Pat's Blog", Before there were four fours..., 2012.
[227] TrueNews.org, "The Origin of Life -- Evolution's Dilemma (web page), accessed 2010 April 29.
[228] Wolfram Alpha, "computational knowledge engine" online resource.
[229] 27: This is close.
[230] Simon Singh, "The Simpsons and Their Mathematical Secrets" (book, 2013) Some of the material is also presented in this article by Singh for The Guardian.
[231] Alexander Reshetov, "A unistable polyhedron with 14 faces." International Journal of Computational Geometry & Applications 24, no. 01 (2014): 39-59.
[232] "MikeMcl", decimal.js, JavaScript library for handling large numbers.
[233] Inder J. Taneja, "Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9" (2014) on arxiv
[234] Washington Taylor and Yi-Nan Wang, "The F-theory geometry with most flux vacua". Journal of High Energy Physics. 2015(12): 164 (2015) on arXiv
[235] John Tromp, "Number of legal Go positions" (2016).
[236] Aarex Tiaokhiao, magna_numerus.js, JavaScript library for handling large numbers (also includes confractus_numerus.js and logarithmica_numerus_lite.js)
[237] "Patashu" (Timothy Stiles), break_infinity.js, JavaScript library for handling large numbers (checkout a commit prior to 2019 March to get the deprecated break_break_infinity.js).
[238] "Patashu" (Timothy Stiles), break_eternity.js, JavaScript library for handling large numbers.
[239] James Read and Baptiste Le Bihan. "The landscape and the multiverse: What's the problem?". Synthese. 199(3–4) 7749–7771 (2021)
[240] Pat Ballew, "Pat's Blog", 2022.
Quick index: if you're looking for a specific number, start with
whichever of these is closest:
0.065988...
1
1.618033...
3.141592...
4
12
16
21
24
29
39
46
52
64
68
89
107
137.03599...
158
231
256
365
616
714
1024
1729
4181
10080
45360
262144
1969920
73939133
4294967297
5×1011
1018
5.4×1027
1040
5.21...×1078
1.29...×10865
1040000
109152051
101036
101010100
— —
footnotes
Also, check out my large numbers
and integer sequences pages.
s.30