32689

32689 is a number that falls between 32688 and 32690 in the sequence of natural numbers. It is an even number, as it is divisible by 2 without leaving a remainder. In the decimal system, it is written as "three-two-six-eight-nine." In Roman numerals, it is represented as "MMMXXCLXXXIX."

The number 32689 has some interesting properties in mathematics. For instance, it is a composite number, meaning it has factors other than 1 and itself. Its prime factorization is 3^2 * 11 * 101. Additionally, 32689 is a sphenic number, which is a product of three distinct prime numbers.

In the context of computing, 32689 is often used as a port number in network communications. Port numbers are used to identify specific processes or services on a computer. The port number 32689 is not assigned to any specific service in the official IANA (Internet Assigned Numbers Authority) port list, but it can be used for custom applications or private use.

In recreational mathematics, 32689 is known for being the smallest number that can be expressed as the sum of two positive cubes in two different ways: 32689 = 30^3 + 1^3 = 29^3 + 16^3. This property makes it an example of a taxicab number, a concept introduced by the mathematician G.H. Hardy.

Overall, 32689 is a number with various mathematical properties and applications, making it an interesting subject for study in both pure and applied mathematics.