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Notable Properties of Specific Numbers    

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[130] 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.

[131] 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.

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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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[158] Don N. Page, Information loss in black holes and/or conscious beings? , 1994. arXiv:hep-th/9411193v2

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[160] James G. Gilson, Calculating the fine structure constant, 1995. PDF here

[161] 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 here

[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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[172] Patrick Costello, A New Largest Smith Number, Fibonacci Quarterly 40(4) 369-371, 2002.

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[175] John Baez, The Fano Plane (web page) 2001. (Part of a collection describing the Octonions)

[176] Palais, Robert. "π Is Wrong!". The Mathematical Intelligencer 23 (3) 7–8 (2001).

[177] David Eberly, Fast inverse square root, 2002 (as archived on 2003 Apr 26 by the Internet Archive Wayback Machine).

[178] Michael Janssen, The Trouton experiment and E=mc2 (handout, PDF file), 2002.

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[180] Toshio Fukushima, A new precession formula. Public Relations Center, NAOJ, 2003.

[181] Chris Lomont, Fast inverse square root, 2003.

[182] Byron Schmuland, "Shouting Factorials!", 23 Oct 2003.

[183] Max Tegmark, Parallel Universes, 2003. Available from

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[185] Dario Alpern, Known 3-digit prime factors of Googolplexplex - 1, web site, 2004.

[186] Sean M. Carroll and Jennifer Chen, Spontaneous Inflation and the Origin of the Arrow of Time, PDF on arXiv

[187] Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe, 2004.

[188] 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] Clifford Pickover. A Passion for Mathematics: numbers, puzzles, madness, religion, and the quest for reality. Wiley (2005). ISBN 0-471-69098-8.

[193] John Baez, Klein's Quartic Curve (web page) July 28, 2006.

[194] Bailey, Borwein, Kapoor and Weisstein, Ten Problems in Experimental Mathematics, American Mathematical Monthly, 2006.

[195] 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

[196] Don N. Page, Susskind's challenge to the Hartle-Hawking no-boundary proposal and possible resolutions, 2006. arXiv:hep-th/0610199v2

[197] Mark Ronan, Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, 2006. ISBN 0-19-280723-4

[198] 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.

[199] David de Neufville, personal correspondence.

[200] John Baez, My Favorite Numbers (web page) 2008. Includes videos and slides from three talks given in 2008 at University of Glasgow.

[201] 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.

[202] My Math Forum, discussion thread, 2008 Oct 10 (formerly at 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.

[203] N. J. A. Sloane, Eight Hateful Sequences, 2008.

[204] Ken Auletta, Googled : the end of the world as we know it (New York : Penguin Press, 2009) ISBN 9781594202353.

[205] Daan van Berkel, On a curious property of 3435. (2009) arXiv:0911.3038

[206] CNN Beat 360, Anderson Cooper Daily Podcast for July 15th, 2009.

[207] Huffington Post, Man Charged 23 Quadrillion..., July 15th, 2009.

[208] Andrei Linde and Vitaly Vanchurin, How many universes are in the multiverse?, 2009. arXiv:0910.1589v2

[209] WMUR TV-9 (Manchester NH), Man's Debit Card Charged $23 Quadrillion..., July 15th, 2009.

[210] Edward L. Wright, Frequently Asked Questions in Cosmology (web page), 2009.

[211] WTOV, Card Users Hit With $23 Quadrillion Charge, July 15th, 2009.

[212] David Eberly, Fast inverse square root (revisited), 2010.

[213] Jeffrey Hankins, personal correspondence, 2010.

[214] 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.")

[215] David Stuart, Notes on Accession Dates in the Inscriptions of Coba, 2010. Available here.

[216] Mark R. Diamond, Multiplicative persistence base 10: some new null results, 2011.

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[220] Bob Delaney, "fp Plugin 5.1", message to realbasic-nug forum (mirror here), 30 Jan 2012

[221] Adam Goucher, Lunisolar calendars (blog article), 2012.

[222] Gottfried Helms, The Lucas-Lehmer-test for Mersenne-numbers and the number Λ ~1.389910663524..., April 4 2012.

[223] 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 525600×6031556952, 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).

[224] Robert Munafo, answer to a question by Mahmud. The relevant discussion is also here: What happens when numbers become large... really large?

[225] "Pat's Blog", Before there were four fours..., 2012.

[226], "The Origin of Life -- Evolution's Dilemma (web page), accessed 2010 April 29.

[227] Wolfram Alpha, "computational knowledge engine" online resource.

[228] 27: This is close.

[229] 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.

[230] Alexander Reshetov, "A unistable polyhedron with 14 faces." International Journal of Computational Geometry & Applications 24, no. 01 (2014): 39-59.

[231] "MikeMcl", decimal.js, JavaScript library for handling large numbers.

[232] 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

[233] 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

[234] John Tromp, "Number of legal Go positions" (2016).

[235] Aarex Tiaokhiao, magna_numerus.js, JavaScript library for handling large numbers (also includes confractus_numerus.js and logarithmica_numerus_lite.js)

[236] "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).

[237] "Patashu" (Timothy Stiles), break_eternity.js, JavaScript library for handling large numbers.

[238] James Read and Baptiste Le Bihan. "The landscape and the multiverse: What's the problem?". Synthese. 199(3–4) 7749–7771 (2021)

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.

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