View source for 4,294,967,295

{{Infobox number
| number = 4294967295
| factorization = 3 × 5 × 17 × 257 × 65537
}}
The [[number]] '''4,294,967,295''' is an [[integer]] equal to 2{{sup|32}}&nbsp;−&nbsp;1. It is a [[perfect totient number]].<ref>{{cite journal|last1=Loomis|first1=Paul|last2=Plytage|first2=Michael|last3=Polhill|first3=John|title=Summing up the Euler φ Function|date=2008|journal=College Mathematics Journal|volume=39|issue=1|pages=34–42|jstor=27646564}}</ref><ref>{{cite journal|author1=Iannucci, Douglas E. |author2=Deng, Moujie |author3=Cohen, Graeme L. | title = On perfect totient numbers | journal = [[Journal of Integer Sequences]] | volume = 6 | year = 2003 | issue = 4 | pages = 03.4.5 |mr=2051959 | url = http://www.emis.de/journals/JIS/VOL6/Cohen2/cohen50.pdf}}</ref> It follows 4,294,967,294 and precedes [[4294967296 (number)|4,294,967,296]]. It has a factorization of <math>3 \cdot 5 \cdot 17 \cdot 257 \cdot 65537</math>.

== In geometry ==
Since the prime factors of 2{{sup|32}}&nbsp;−&nbsp;1 are exactly the five known [[Fermat prime]]s, this number is the largest known odd value ''n'' for which a [[regular polygon|regular]] [[n-gon|''n''-sided polygon]] is [[constructible polygon|constructible using compass and straightedge]].<ref>{{cite book|last1=Lines|first1=Malcolm E|title=A Number for your Thoughts: Facts and Speculations About Numbers from Euclid to the latest Computers...|date=1986|publisher=Taylor & Francis|isbn=9780852744956|page=17|edition=2}}</ref><ref name="OEIS">{{Cite OEIS|sequencenumber=A004729 |name=Divisors of 2^32 - 1 (for a(1) to a(31), the 31 regular polygons with an odd number of sides constructible with ruler and compass)}}</ref> Equivalently, it is the largest known odd number ''n'' for which the angle <math>2\pi/n</math> can be constructed, or for which <math>\cos(2\pi/n)</math> can be expressed in terms of [[square root]]s.

Not only is 4,294,967,295 the largest known odd number of sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers ''n'' for which an ''n''-sided polygon is constructible begins with the list of factors of 4,294,967,295. If there are no more Fermat primes, then the two lists are identical. Namely (assuming 65537 is the largest Fermat prime), an odd-sided polygon is constructible if and only if it has 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, or 4294967295 sides.<ref name="OEIS"/> If there are more numbers in this list, they must be at least 2{{sup|2{{sup|33}}}}+1 (approximately 10{{sup|2585827973}}), because every intervening Fermat number is known to be composite.<ref>{{cite url|url=http://mathworld.wolfram.com/FermatNumber.html|title=Fermat Number|publisher=Wolfram MathWorld}}</ref>

== In computing ==

The number 4,294,967,295, equivalent to the [[hexadecimal]] value {{nowrap|FFFF,FFFF{{sub|16}}}}, is the maximum value for a [[32-bit]] [[integer (computer science)|unsigned integer]] in [[computing]].<ref>{{cite book|last1=Simpson|first1=Alan|title=Alan Simpson's Windows XP bible|date=2005|publisher=J. Wiley|location=Indianapolis, Indiana|isbn=9780764588969|page=999|edition=2nd|chapter=58: Editing the Windows Registry}}</ref> It is therefore the maximum value for a [[variable (computer science)|variable]] declared as an unsigned integer (usually indicated by the {{code|unsigned}} codeword) in many programming languages running on modern computers. The presence of the value may reflect an error, overflow condition, or missing value.

This value is also the largest [[computer memory|memory]] address for CPUs using a 32-bit address bus.<ref>{{cite web|last1=Spector |first1=Lincoln |title=Why can't 32-bit Windows access 4GB of RAM? |url=http://www.pcworld.com/article/2013751/why-cant-32-bit-windows-access-4gb-of-ram.html |website=PC World |publisher=IDG Consumer & SMB |archiveurl=https://www.webcitation.org/6fmPvN0iW?url=http://www.pcworld.com/article/2013751/why-cant-32-bit-windows-access-4gb-of-ram.html |archivedate=5 March 2016 |date=19 November 2012 |url-status=live }}</ref> Being an odd value, its appearance may reflect an erroneous (misaligned) memory [[pointer (computer programming)|address]]. Such a value may also be used as a [[magic debug values|sentinel value]] to initialize newly allocated memory for debugging purposes.

== See also ==
* [[Magic number (programming)]]
* [[2147483647 (number)]]
* [[Power of two]]
* [[Equilateral triangle]]
* [[Pentagon]]
* [[Heptadecagon]] (17-sides)
* [[257-gon]]
* [[65537-gon]]

==References==
{{reflist}}

{{DEFAULTSORT:4294967295}}
[[Category:Integers]]
[[Category:Constructible polygons]]