65,536

65536 is the natural number following 65535 and preceding 65537.

← 65535 65536 65537 →
← 0 [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]]
Cardinalsixty-five thousand five hundred thirty-six
Ordinal65536th
(sixty-five thousand five hundred thirty-sixth)
Factorization216
Divisors17 total
Greek numeral͵εφλϚ´
Roman numeralLXVDXXXVI
Binary100000000000000002
Ternary100222200213
Octal2000008
Duodecimal31B1412
Hexadecimal1000016

65536 is a power of two: (2 to the 16th power).

65536 is the smallest number with exactly 17 divisors.[1]

In mathematics

65536 is , so in tetration notation 65536 is 42.

When expressed using Knuth's up-arrow notation, 65536 is , which is equal to , which is equivalent to or .

65536 is a superperfect number – a number such that σ(σ(n)) = 2n.[2]

A 16-bit number can distinguish 65536 different possibilities. For example, unsigned binary notation exhausts all possible 16-bit codes in uniquely identifying the numbers 0..65535. In this scheme, 65536 is the least natural number that can not be 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 231000 that does not contain the digits 1, 2, 4 or 8 in its decimal representation.[3]

65536 is the largest known number such that the sum of its unitary divisors is prime (1 + 65536 = 65537, which is prime).[4]

65536 is an untouchable number.

In computing

65536 (216) is the number of different values representable in a number of 16 binary digits (or bits), also known as an unsigned short integer in many computer programming systems. This can place a limitation on many common hardware and software implementations, some examples of which are:

  • The Motorola 68000 family, x86 architecture, and other computing platforms have a word size of 16 bits, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern microprocessors.)
  • Many modern CPUs allow a memory page size of 64KiB (65536 bytes) to be configured in their memory-management hardware.[5]
  • 65536 is the maximum number of spreadsheet rows supported by Excel 97, Excel 2000, Excel 2002 and Excel 2003. Text files that are larger than 65536 rows cannot be imported to these versions of Excel.[6] (Excel 2007, 2010 and 2013 support 1,048,576 rows (220)).
  • A 16-bit microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors.
  • The maximum number of methods allowed in a single dex file Android application is 65536.[7]
  • 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 a network address to create a network socket.
  • The maximum character limit for one message in WhatsApp is 65536.
  • There are 65536 different charts in Western geomancy.
gollark: So what... training library/model implementation, I guess... isn't bad?
gollark: I doubt that would work for training very well.
gollark: Yes. It seemed easiest.
gollark: The 350M one doesn't seem to exist and I can't really work with anything bigger.
gollark: This is annoying, apparently 6GB of VRAM isn't enough to finetune the 125M GPT-Neo even with a batch size of 1. I might just use Colab.

References
  1. Sloane, N. J. A. (ed.). "Sequence A005179". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. Weisstein, Eric W. "Superperfect Number". MathWorld.
  3. Wells, David (1997). The Penguin Dictionary of Curious and Interesting Numbers (revised ed.). Penguin. ISBN 0-14-026149-4.
  4. 65536 at Prime Pages
  5. "General Purpose Operating System Support for Multiple Page Sizes" (PDF). static.usenix.org. Retrieved 2012-11-02.
  6. Microsoft Help Q120596
  7. http://developer.android.com/tools/building/multidex.html
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