65,535 (number)

65 535 is an odd five - digit squareless number.

• Is composite : 65 535 = 3 × 5 × 17 × 257.
• The sum of the digits of the number 65 535 is 24 , the product of the digits is 2,250.

Interesting mathematical properties:

• 65 535 is the Mersenne number ^[1] : 65 535 = 2 ¹⁶ - 1.
• The factorization of 65,535 consists of the first four Fermat primes - 3, 5, 17 and 257.
  • Due to this property, you can build a regular polygon with 65,535 sides using only the compass and the ruler.
• 65,535 is a 15,626-angular number , a fifth 6,555-angular number and a third 21,846-angular number.

The number 65,535 is often found in the field of computer technology as the largest unsigned integer with a machine word length of 2 bytes (16 bits). On older computers with processors with a 16-bit address bus (for example, MOS Technology 6502 and Zilog Z80 ), the value 65,535 ( FFFF in hexadecimal notation ) corresponds to the address of the last addressable memory location . Thus, this type of processor supports no more than 64 kbytes of byte-addressable shared memory .

In the Internet protocols TCP and UDP, the number of ports available for use is also limited by the number 65 535 , since port number 0 reserved.

In many environments and programming languages, fixed values equal to 65,535 are predefined with identifiers such as MAX_UNSIGNED_SHORT and the like, indicating the upper limit of a particular type of integer (in this case, a subset of non-negative integers starting from zero and matching into a two-byte machine word). The existence of such subtypes is also due to the history of computer development.

Some other limitations and conventions associated with the use of this number in the design of environments and programming languages:

• A class or interface in the Java language can have no more than 65,535 methods. The constructor code in Java is limited to 65,535 bytes.
• The .charCodeAt(i) method .charCodeAt(i) (ECMAScript) returns the number corresponding to the character of the string with index i and with the maximum possible value of 65,535 .
• In some BASIC implementations, entering a command that divides any number by zero will return 65,535 .

The aforementioned features of the low-level software implementation are due to the emergence of the number 65 535 in applications for the end user, usually also in the form of certain limitations of their functionality:

• In Microsoft Word 2011 and Numbers for MacOS, the number of rows displayed in a document or spreadsheet is limited to 65,535 .
• In the unpatched version of the spreadsheet processor Microsoft Excel 2007, some mathematical calculations with the results in the vicinity of 65,535 were displayed incorrectly. For example, the result of displaying the formula =850*77.1 was 100,000 instead of 65,535 . Microsoft stated [1] that this error is only reproduced for 6 floating-point numbers between 65,535 and 65,536 . In Microsoft Excel 2007 Service Pack 2 and older versions of this program, this type of error was resolved.

• 16 bit
• 4294967295
• 255 (number)

• The number 65 535 in OEIS ( all results )
• Number 65 535 / site AboutNumber.ru
• Properties of the number 65,535 / Empire of Numbers site
• The number 65 535 in detail
• Declension of 65 535 cases
• Microsoft Blog