288 (two hundred [and] eighty-eight) is thenatural number following287 and preceding289.Because 288 = 2 · 12 · 12, it may also be called "twogross" or "two dozen dozen".
Both 288 and289 = 172 arepowerful numbers, numbers in which all exponents of the prime factorization are larger than one.[5][6][7] This property is closely connected to being highly abundant with an odd divisor sum: all sufficiently large highly abundant numbers have an odd prime factor with exponent one, causing their divisor sum to be even.[4][8] 288 and 289 form only the second consecutive pair of powerful numbers after8 and 9.[5][6][7]
288 is asuperfactorial, a product of consecutivefactorials, since[5][9][10] Coincidentally, as well as being a product of descending powers, 288 is a sum of ascending powers:[11]
288 appears prominently inStirling's approximation for the factorial, as the denominator of the second term of the Stirling series[12]
There are 288 different ways of completely filling in asudoku puzzle grid.[17][18] For square grids whose side length is the square of a prime number, such as 4 or 9, a completed sudoku puzzle is the same thing as a "pluperfect Latin square", an array in which every dissection into rectangles of equal width and height to each other has one copy of each digit in each rectangle. Therefore, there are also 288 pluperfect Latin squares of order 4.[19] There are 288 differentinvertible matrices modulo six,[20] and 288 different ways of placing two chess queens on a board with toroidal boundary conditions so that they do not attack each other.[21] There are 288independent sets in a 5-dimensional hypercube, up to symmetries of the hypercube.[22]
In early 20th-centurymolecular biology, some mysticism surrounded the use of 288 to countprotein structures, largely based on the fact that it is a smooth number.[23][24]
A common mathematicalpun involves the fact that288 = 2 · 144, and that 144 is named as agross: "Q: Why should the number 288 never be mentioned? A: it is two gross."[25]
^Potter, Robert D. (February 12, 1938). "Building blocks of life ruled by the number 288: This number and its multiples found everywhere in groupings of amino acids to form proteins".The Science News-Letter.33 (7):99–100.doi:10.2307/3914385.JSTOR3914385.
^Nowlan, Robert A. (2017). "Logical Nonsense".Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them. Sense Publishers. pp. 263–268.doi:10.1007/978-94-6300-893-8_17.ISBN978-94-6300-893-8. See p. 284.
