65,536

← 65535 65536 65537 →
List of numbers Integers ←010k20k30k40k50k60k70k80k90k→
Cardinal	sixty-five thousand five hundred thirty-six
Ordinal	65536th (sixty-five thousand five hundred thirty-sixth)
Factorization	216
Divisors	1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536
Greek numeral	${\stackrel {\digamma }{\mathrm {M} }}$͵εφλϚ´
Roman numeral	LXVDXXXVI
Binary	100000000000000002
Ternary	100222200213
Senary	12232246
Octal	2000008
Duodecimal	31B1412
Hexadecimal	1000016

65536is thenatural numberfollowing65535and preceding65537.

65536 is apower of two:$2^{16}$(2 to the 16th power).

65536 is the smallest number with exactly 17divisors(but there are smaller numbers with more than 17 divisors; e.g.,180has 18 divisors) (sequenceA005179in theOEIS).

256×256 grid with 65536 squares

In mathematics

65536 is$2^{2^{2^{2}}}$,so intetrationnotation 65536 is⁴2.

When expressed usingKnuth's up-arrow notation,65536 is $2\uparrow 16$, which is equal to $2\uparrow 2\uparrow 2\uparrow 2$, which is equivalent to $2\uparrow \uparrow 4$ or $2\uparrow \uparrow \uparrow 3$.

As$^{2}2$is also equal to 4, or$2\uparrow \uparrow 2=4$,

$^{4}2$can thus be written as$^{^{2}2}2$, or$2\uparrow \uparrow (2\uparrow \uparrow 2)$,or as the pentation,$2[5]3$(hyperoperation notation).

65536 is asuperperfect number– a number such thatσ(σ(n)) = 2n.

A16-bitnumber can distinguish 65536 different possibilities. For example,unsignedbinary notationexhausts all possible 16-bit codes in uniquely identifying the numbers 0 to 65535. In this scheme, 65536 is the leastnatural numberthat cannotbe represented with 16 bits. Conversely, it is the "first" or smallest positive integer that requires 17 bits.

65536 is the only power of 2 less than 2³¹⁰⁰⁰that does not contain the digits 1, 2, 4, or 8 in itsdecimal representation.

The sum of theunitary divisorsof 65536 is prime (1 + 65536 =65537,which is prime).

65536 is anuntouchable number.

In computing

65,536 (2¹⁶) is the number of different values representable in a number of 16binary digits(orbits), also known as anunsigned short integerin manycomputer programmingsystems.

• A 65,536-bit integer can represent up to 2^65,536(2.00352993...×10^19,728) values.
• 65,536 is the number of characters in the originalUnicode,and currently in a Unicode plane.

This number is a limit in many common hardware and software implementations, some examples of which are:

• TheMotorola 68000 family,x86 architecture,and othercomputing platformshave awordsize of 16bits,representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modernmicroprocessors.)
• Many modern CPUs allow amemory pagesize of 64KiB(65536 bytes) to be configured in theirmemory-management hardware.
• The default buffer size of apipeline (Unix)is 64KiB (65536 bytes).
• 65536 is the maximum number of spreadsheet rows supported byExcel97, Excel 2000, Excel 2002 and Excel 2003. Text files that are larger than 65536 rows cannot be imported to these versions of Excel.(Excel 2007, 2010 and 2013 support1,048,576rows (2²⁰)).
• A16-bitmicroprocessor chip can directly access 65536 memory addresses, and the16-bit highcolorgraphics standard supports a color palette of 65536 different colors.
• The maximum number of methods allowed in a single dex file Android application is 65536.
• The limit for the amount of code in bytes for a non-native, non-abstract method in Java.
• The number of available ports to combine with anetwork addressto create anetwork socket.
• The maximum character limit for one message inWhatsAppis 65536.