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Mathematical coincidence
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=== Other numerical curiosities === * In a discussion of the [[birthday problem]], the number <math>\lambda=\frac{1}{365}{23\choose 2}=\frac{253}{365}</math> occurs, which is "amusingly" equal to <math>\ln(2)</math> to 4 digits.<ref> {{cite journal | last1 = Arratia | first1 = Richard | author1-link = Richard Arratia | last2 = Goldstein | first2 = Larry | last3 = Gordon | first3 = Louis | issue = 4 | journal = [[Statistical Science]] | jstor = 2245366 | mr = 1092983 | pages = 403β434 | title = Poisson approximation and the Chen-Stein method | volume = 5 | year = 1990 | doi=10.1214/ss/1177012015| doi-access = free }}</ref> * <math>5 \cdot 10^5 - 1 = 31 \cdot 127 \cdot 127</math>, the product of three [[Mersenne primes]].<ref>{{cite web|url=https://primes.utm.edu/curios/page.php/499999.html|title=Prime Curios! 499999|publisher = Prime Curios}}</ref> * <math>\sqrt[6]{6!}</math>, the [[geometric mean]] of the first 6 natural numbers, is approximately 2.99; that is, <math>6! = 720 \approx 729 = 3^6</math>. * The sixth [[harmonic number]], <math display="block">H_6= 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6} = \frac{49}{20} = 2.45</math> which is approximately <math>\sqrt{6}</math> (2.449489...) to within 5.2 Γ 10<sup>β4</sup>. * <math>\sqrt[5]{109} \approx \frac{23}{9}</math>, within <math>2 \times 10^{-7}</math>.<ref>[https://web.archive.org/web/20191104071738/https://www2.stetson.edu/~efriedma/numbers.html What's Special About This Number?] (archived)</ref> Equivalently, <math>2.5555555^{5} \approx 109</math>, within 2.2 Γ 10<sup>β5</sup>.
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