9855

9855 (nine thousand eight hundred fifty-five) is the natural number following 9854 and preceding 9856. An odd and composite number, its prime factors are 3, 5, and 73 and its prime factorization is:

${\displaystyle 9855=3^{3}\times 5\times 73}${\displaystyle 9855=3^{3}\times 5\times 73}.

It is the sum of all the numbers in any given row, column, or diagonal of the 27 ×ばつ 27 magic square,^{[1] [2]} as shown in the following calculation:

${\displaystyle 9855={\frac {1}{27}}\sum _{k=1}^{27^{2}}k={\frac {27\times (27^{2}+1)}{2}}}${\displaystyle 9855={\frac {1}{27}}\sum _{k=1}^{27^{2}}k={\frac {27\times (27^{2}+1)}{2}}}

The 27 ×ばつ 27 magic square contains 1 to 729, with 365 in the center.^[2]

9855 is also the number of days in 27 years; C.A. Brown hypothesized in a 1906 edition of The Monist that this number could have held a significance for Ancient Greeks as the "dividing line between the ages when men and women should begin to bear children to the State, 20-27 years for women, 27-34 years for men"^[2]

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