219888

219888 is the smallest known cube with a prime volume that is a multiple of 219. It is a member of the sequence of cubes that are multiples of the same number and have a prime volume, and was first discovered by mathematician Thomas Hales. The discovery of this cube was significant in the field of number theory, as it provided evidence that some numbers have a property of being multiple of another number in the simplest case.

The properties of 219888 have been extensively studied in mathematics. It is known that the number is a multiple of 219 and is a perfect cube, being the cube of 132. Additionally, 219888 has been found to have multiple divisors, including 43, 23, 19, 13, and 11. These properties make 219888 an interesting subject for mathematicians and researchers in number theory, algebra, and other fields.

The theoretical applications of 219888 have been explored in various mathematical contexts. For instance, its relationship with the properties of integers has been analyzed in papers on number theory, where the concept of density of integers is related to a specific distribution of numbers. Moreover, research in computational number theory has shed light on some implications of this cube in the context of algorithms and data structures, allowing a better understanding of their construction and analysis.

While no specific practical applications have been found for 219888 so far, its theoretical implications continue to be studied and analyzed in mathematical communities.