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<p><b>新页面</b></p><div>{{NoteTA<br />
|G1=Math<br />
|G2=IT<br />
}}<br />
{{整数<br />
| list = <br/>2147483646 - '''2147483647''' - 2147483648<br/>{{Numbers digits|1|last=0|next=大数_(数学)|template=#invoke:NumberUtil{{!}}exp10link}}<br />
| 质数 = 第105097565個<br />
| 罗马数字 = <math>\overline{\overline\mathrm{MMCXLV}}\overline\mathrm{MMCDLXXX}\mathrm{MMMDCXLVII}</math><br />
}}<br />
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'''2,147,483,647'''是2147483646與2147483648之間的[[自然數]]。它等于<math>2^{31} - 1</math>。它是第8个[[梅森素数]]，也是4個已知的[[双重梅森素数]]的其中一個。<br />
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[[欧拉]]在1772年用[[试除法]]判定这个数是梅森素数。<ref>{{cite book |first=Walter |last=Gautschi |title=Mathematics of Computation, 1943–1993: A Half-Century of Computational Mathematics |location=Providence, Rhode Island |publisher=[[American Mathematical Society]] |series=Proceedings of Symposia in Applied Mathematics |volume=48 |year=1994 |page=486 |isbn=978-0-8218-0291-5}}</ref><ref>{{cite book |first=William |last=Dunham |title=Euler: The Master of Us All |url=https://archive.org/details/eulermasterofusa0000dunh_b9h6 |url-access=registration |location=Washington, DC |publisher=Mathematical Association of America |year=1999 |page=[https://archive.org/details/eulermasterofusa0000dunh_b9h6/page/4 4] |isbn=978-0-88385-328-3}}</ref>在1772年至1867年期间这个数是已知的最大[[素数]]。<ref name="The Largest Known Prime by Year">{{cite web |last=Caldwell |first=Chris |date=8 December 2009 |url=http://primes.utm.edu/notes/by_year.html |title=The Largest Known Prime by Year: A Brief History |website=The Prime Pages |publisher=University of Tennessee at Martin |access-date=January 29, 2018 |archive-date=2020-06-05 |archive-url=https://web.archive.org/web/20200605042826/http://primes.utm.edu/notes/by_year.html }}</ref><br />
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这个数表示为二进制为1111111111111111111111111111111（即31個1），是[[操作系统]]中最大的[[32位元]][[有符号数|符号型]]整型常量，例如[[Pascal語言]]中[[长整型]]的範圍是-2147483648~2147483647。<br />
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== YouTube计数器事件 ==<br />
2014年12月，谷歌宣称因[[YouTube]]上[[觀看次數最多的YouTube影片列表|播放次数最多的视频]]，[[PSY]]的《[[江南Style]]》[[音乐视频]]的播放次数超过了播放计数器的最大值（32位正负整型，即2147483647），导致YouTube不得不将播放计数器升级至[[64位]]整型。<ref>{{Cite web|url =https://plus.google.com/u/0/wm/4/+youtube/posts/BUXfdWqu86Q|title =Gangnam Style YouTube Overflow|date =|accessdate =|website =|publisher =|last =|first =|deadurl =yes|archiveurl =https://archive.today/20141203224157/https://plus.google.com/u/0/wm/4/+youtube/posts/BUXfdWqu86Q|archivedate =2014-12-03}}</ref> 后来谷歌承认这是一个玩笑。<ref>{{Cite web|url = http://www.cnet.com/news/gangnam-style-busts-youtubes-view-counter-not-so-fast/|title = Gangnam Style YouTube Overflow revisit|date = |accessdate = |website = |publisher = |last = |first = |archive-url = https://web.archive.org/web/20151030121756/http://www.cnet.com/news/gangnam-style-busts-youtubes-view-counter-not-so-fast/|archive-date = 2015-10-30|dead-url = yes}}</ref><br />
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== 参见 ==<br />
*[[2的幂]]<br />
*[[4294967295]]<br />
==參考資料==<br />
{{Reflist}}<br />
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[[Category:整數素數|億位]]<br />
[[Category:整数]]<br />
[[Category:梅森素数]]</div>
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