查看“︁100000000”︁的源代码

{{noteTA|G1=Math}}
{{整数
| list = {{Numbers digits|1|last=0|next=大数_(数学)|template=#invoke:NumberUtil{{!}}exp10link}}<br/>[[10000000]] '''100000000''' [[1000000000]]
| 罗马数字 = <math>\overline\overline{\mathrm{C}}</math>
}}
'''100,000,000''' （'''一亿'''）是99,999,999和100,000,001之间的[[自然数]]。

用[[科学记数法]]写成 10<sup>8</sup> 。

东亚语言将“[[亿]]”作为一个计数单位，相当另一个计数单位“[[万]]”的平方。在韩文和日文中分别为 ''eok'' ( {{Lang|ko|억/億}}) 和''oku'' ({{Nihongo2|億}}）。

100,000,000是[[100]]的[[四次方數|四次方]]，也是[[10000]]的[[平方]]。

== 值得注意的 9 位数字 (100,000,001–999,999,999) ==

=== 100,000,001 至 199,999,999 ===

* 100,000,007 = 最小的九位素数<ref name="A003617">{{SloanesRef|A003617|Smallest n-digit prime|access-date=7 September 2017}}</ref>
* 100,005,153 = 最小的 9 位[[三角形數|三角数]]和第 14,142 个三角数
* 100,020,001 = 10001<sup>2</sup>, 回文平方
* 100,544,625 = 465<sup>3</sup> ，最小的9位立方
* 102,030,201 = 10101<sup>2</sup>，回文平方
* 102,334,155 = [[斐波那契数列|斐波那契数]]
* 102,400,000 = 40<sup>5</sup>
* 104,060,401 = 10201<sup>2</sup> = 101<sup>4</sup> ，回文平方
* 105,413,504 = 14<sup>7</sup>
* 107,890,609 = [[韦德伯恩-埃瑟林顿数]]<ref name=":0" />
* 111,111,111 = [[循環單位]], 12345678987654321 的平方根
* 111,111,113 = [[陈素数]]、苏菲杰曼素数、[[表兄弟素数|表弟素数]]。
* 113,379,904 = 10648<sup>2</sup> = 484<sup>3</sup> = 22<sup>6</sup>
* 115,856,201 = 41<sup>5</sup>
* 119,481,296 = 对数<ref>{{SloanesRef|A002104|Logarithmic numbers}}</ref>
* 121,242,121 = 11011<sup>2</sup>, 回文平方
* 123,454,321 = 11111<sup>2</sup>, 回文平方
* 123,456,789 = 最小无零基 10 [[泛位數|泛数字]]
* 125,686,521 = 11211<sup>2</sup>, 回文平方
* 126,390,032 = 补数相等的 34 珠项链数量（允许翻转） <ref name="未命名-20231105161103">{{SloanesRef|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
* 126,491,971 = 莱昂纳多素数
* 129,140,163 = 3<sup>17</sup>
* 129,145,076 = 利兰数
* 129,644,790 = [[卡塔兰数|加泰罗尼亚号码]]<ref name=":1" />
* 130,150,588 = 33 珠二元项链的数量，有 2 种颜色的珠子，颜色可以互换，但不允许翻转<ref name="未命名_2-20231105161103">{{SloanesRef|A000013|Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed}}</ref>
* 130,691,232 = 42<sup>5</sup>
* 134,217,728 = 512<sup>3</sup> = 8<sup>9</sup> = 2<sup>27</sup>
* 134,218,457 = 利兰数
* 136,048,896 = 11664<sup>2</sup> = 108<sup>4</sup>
* 139,854,276 = 11826<sup>2</sup> ，最小无零底数 10 泛数字平方
* 142,547,559 = [[默慈金數|莫茨金数]]<ref name=":2" />
* 147,008,443 = 43<sup>5</sup>
* 148,035,889 = 12167<sup>2</sup> = 529<sup>3</sup> = 23<sup>6</sup>
* 157,115,917 – 24 个单元的平行四边形多格骨牌的数量。 <ref name="未命名_3-20231105161103">{{SloanesRef|A006958|Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)}}</ref>
* 157,351,936 = 12544<sup>2</sup> = 112<sup>4</sup>
* 164,916,224 = 44<sup>5</sup>
* 165,580,141 = [[斐波那契数列|斐波那契数]]
* 167,444,795 = [[六进制|6 进制]]下的[[循环数]]
* 170,859,375 = 15<sup>7</sup>
* 171,794,492 = 具有 36 个节点的缩减树的数量<ref name="未命名_4-20231105161103">{{SloanesRef|A000014|Number of series-reduced trees with n nodes}}</ref>
* 177,264,449 = 利兰数
* 179,424,673 = 第 10,000,000 个[[质数]]
* 184,528,125 = 45<sup>5</sup>
* 188,378,402 = 划分{1,2,...,11}然后将每个单元（块）划分为子单元的方式数。 <ref>{{SloanesRef|A000258|Expansion of e.g.f. exp(exp(exp(x)-1)-1)}}</ref>
* 190,899,322 = [[贝尔数]]<ref>{{Cite web|title=Sloane's A000110 : Bell or exponential numbers|url=https://oeis.org/A000110|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2019-08-30|archive-url=https://web.archive.org/web/20190830062932/http://oeis.org/A000110|dead-url=no}}</ref>
* 191,102,976 = 13824<sup>2</sup> = 576<sup>3</sup> = 24<sup>6</sup>
* 192,622,052 = 自由 18 格[[多格骨牌|骨牌]]的数量
* 199,960,004 = 边长为 9999 的四面体的表面点数<ref name="未命名_5-20231105161103">{{SloanesRef|A005893|Number of points on surface of tetrahedron}}</ref>

=== 200,000,000 至 299,999,999 ===

* 200,000,002 = 边长为 10000 的四面体的表面点数<ref name="未命名_5-20231105161103"/>
* 205,962,976 = 46<sup>5</sup>
* 210,295,326 = Fine's number
* 211,016,256 = GF(2) 上的 33 次本原多项式的数量<ref name="未命名_6-20231105161103">{{SloanesRef|A011260|Number of primitive polynomials of degree n over GF(2)}}</ref>
* 212,890,625 = 1-[[自守数]]<ref name="automorphic" />
* 214,358,881 = 14641<sup>2</sup> = 121<sup>4</sup> = 11<sup>8</sup>
* 222,222,222 = [[純位數]]
* 222,222,227 = 安全素数
* 223,092,870 = 前九个[[质数|素数]]的乘积，即第九个[[質數階乘|素数]]
* 225,058,681 = [[佩尔数]]<ref name=":3" />
* 225,331,713 = 以 9 为基数的自描述数字
* 229,345,007 = 47<sup>5</sup>
* 232,792,560 = 高级高合数； <ref name="未命名_7-20231105161103">{{Cite web|title=Sloane's A002201 : Superior highly composite numbers|url=https://oeis.org/A002201|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2010-12-29|archive-url=https://web.archive.org/web/20101229032520/https://oeis.org/A002201|dead-url=no}}</ref>[[可羅薩里過剩數]]； <ref name="未命名_8-20231105161103">{{Cite web|title=Sloane's A004490 : Colossally abundant numbers|url=https://oeis.org/A004490|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2012-05-25|archive-url=https://web.archive.org/web/20120525075430/https://oeis.org/A004490|dead-url=no}}</ref>可被 1 到 22 所有数字整除的最小数字
* 244,140,625 = 15625<sup>2</sup> = 125<sup>3</sup> = 25<sup>6</sup> = 5<sup>12</sup>
* 244,389,457 = 利兰数
* 244,330,711 = n 使得 n | (3<sup>n</sup> + 5) 
* 245,492,244 = 补数相等的 35 珠项链数量（允许翻转） <ref name="未命名-20231105161103"/>
* 252,648,992 = 34 珠二元项链的数量，有 2 种颜色的珠子，颜色可以互换，但不允许翻转<ref name="未命名_2-20231105161103"/>
* 253,450,711 = 韦德伯恩-埃瑟林顿素数<ref name=":0" />
* 254,803,968 = 48<sup>5</sup>
* 267,914,296 = [[斐波那契数列|斐波那契数]]
* 268,435,456 = 16384<sup>2</sup> = 128<sup>4</sup> = 16<sup>7</sup> = 4<sup>14</sup> = 2<sup>28</sup>
* 268,436,240 = 利兰数
* 268,473,872 = 利兰数
* 272,400,600 = 通过 20 所需的[[调和级数]]的项数
* 275,305,224 = 5 阶[[幻方]]的数量，不包括旋转和反射
* 282,475,249 = 16807<sup>2</sup> = 49<sup>5</sup> = 7<sup>10</sup>
* 292,475,249 = 利兰数

=== 300,000,000 至 399,999,999 ===

* 308,915,776 = 17576<sup>2</sup> = 676<sup>3</sup> = 26<sup>6</sup>
* 312,500,000 = 50<sup>5</sup>
* 321,534,781 = 马尔可夫素数
* 331,160,281 = 莱昂纳多素数
* 333,333,333 = [[純位數]]
* 336,849,900 = GF(2) 上的 34 次本原多项式的数量<ref name="未命名_6-20231105161103"/>
* 345,025,251 = 51<sup>5</sup>
* 350,238,175 = 具有 37 个节点的缩减树的数量<ref name="未命名_4-20231105161103"/>
* 362,802,072 = 25 个单元的平行四边形多格骨牌数量<ref name="未命名_3-20231105161103"/>
* 364,568,617 = 利兰数
* 365,496,202 = n 使得 n | (3<sup>n</sup> + 5) 
* 367,567,200 = [[可羅薩里過剩數]]，{{link-en|Superior highly composite number}}
* 380,204,032 = 52<sup>5</sup>
* 381,654,729 = 唯一[[累进可除数]]，同时也是无零泛[[泛位數|泛位数]]
* 387,420,489 = 19683<sup>2</sup> = 729<sup>3</sup> = 27<sup>6</sup> = 9<sup>9</sup> = 3<sup>18</sup>，[[迭代冪次|迭代幂次]]表示为 <sup>2</sup>9
* 387,426,321 = 利兰数

=== 400,000,000 至 499,999,999 ===

* 400,080,004 = 20002<sup>2</sup>, 回文平方
* 400,763,223 = 莫茨金数<ref name=":2">{{SloanesRef|A001006|Motzkin numbers|access-date=2016-06-17}}<cite class="citation web cs1" data-ve-ignore="true" id="CITEREFSloane_&quot;A001006&quot;">[[尼爾·斯洛恩|Sloane, N.&nbsp;J.&nbsp;A.]] (ed.). [[oeis:A001006|"Sequence&#x20;A001006&#x20;(Motzkin numbers)"]]. ''The [[整數數列線上大全|On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-17</span></span>.</cite></ref>
* 404,090,404 = 20102<sup>2</sup>, 回文平方
* 405,071,317 = 1<sup>1</sup> + 2<sup>2</sup> + 3<sup>3</sup> + 4<sup>4</sup> + 5<sup>5</sup> + 6<sup>6</sup> + 7<sup>7</sup> + 8<sup>8</sup> + 9<sup>9</sup>
* 410,338,673 = 17<sup>7</sup>
* 418,195,493 = 53<sup>5</sup>
* 429,981,696 = 20736<sup>2</sup> = 144<sup>4</sup> = 12<sup>8</sup> = 100,000,000 <sub>12</sub>又名gross-great-great-gross (100 <sub>12</sub> Great-great-grosses)
* 433,494,437 = [[費波那契質數|斐波那契素数]]、马尔可夫素数
* 442,386,619 = 交替阶乘<ref>{{Cite web|title=Sloane's A005165 : Alternating factorials|url=https://oeis.org/A005165|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2012-10-09|archive-url=https://web.archive.org/web/20121009005134/https://oeis.org/A005165|dead-url=no}}</ref>
* 444,101,658 = 具有 27 个节点的（无序、无标签）有根修剪树的数量<ref>{{SloanesRef|A002955|Number of (unordered, unlabeled) rooted trimmed trees with n nodes}}</ref>
* 444,444,444 = [[純位數]]
* 455,052,511 = 10以下的素数个数<sup>10</sup>
* 459,165,024 = 54<sup>5</sup>
* 467,871,369 = 14 个顶点上的无三角形图的数量<ref>{{SloanesRef|A006785|Number of triangle-free graphs on n vertices}}</ref>
* 477,353,376 = 补数相等的 36 珠项链数量（允许翻转） <ref name="未命名-20231105161103"/>
* 477,638,700 = 加泰罗尼亚号码<ref name=":1">{{SloanesRef|A000108|Catalan numbers|access-date=2016-06-17}}<cite class="citation web cs1" data-ve-ignore="true" id="CITEREFSloane_&quot;A000108&quot;">[[尼爾·斯洛恩|Sloane, N.&nbsp;J.&nbsp;A.]] (ed.). [[oeis:A000108|"Sequence&#x20;A000108&#x20;(Catalan numbers)"]]. ''The [[整數數列線上大全|On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-17</span></span>.</cite></ref>
* 479,001,599 = [[阶乘素数|阶乘质数]]<ref>{{Cite web|title=Sloane's A088054 : Factorial primes|url=https://oeis.org/A088054|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2020-10-03|archive-url=https://web.archive.org/web/20201003011250/https://oeis.org/A088054|dead-url=no}}</ref>
* 479,001,600 = 12！
* 481,890,304 = 21952<sup>2</sup> = 784<sup>3</sup> = 28<sup>6</sup>
* 490,853,416 = 35 珠二元项链的数量，有 2 种颜色的珠子，颜色可以交换，但不允许翻转<ref name="未命名_2-20231105161103"/>
* 499,999,751 = 苏菲·杰曼素数

=== 500,000,000 至 599,999,999 ===

* 503,284,375 = 55<sup>5</sup>
* 522,808,225 = 22865<sup>2</sup>, 回文平方
* 535,828,591 = 莱昂纳多素数
* 536,870,911 = 第三个具有质数指数的复合[[梅森素数|梅森数]]
* 536,870,912 = 2<sup>29</sup>
* 536,871,753 = 利兰数
* 542,474,231 = k 使得前 k 个素数的平方和可被 k 整除。 <ref>{{SloanesRef|A111441|Numbers k such that the sum of the squares of the first k primes is divisible by k|access-date=2022-06-02}}</ref>
* 543,339,720 = 佩尔号<ref name=":3">{{SloanesRef|A000129|Pell numbers|access-date=2016-06-17}}<cite class="citation web cs1" data-ve-ignore="true" id="CITEREFSloane_&quot;A000129&quot;">[[尼爾·斯洛恩|Sloane, N.&nbsp;J.&nbsp;A.]] (ed.). [[oeis:A000129|"Sequence&#x20;A000129&#x20;(Pell numbers)"]]. ''The [[整數數列線上大全|On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-17</span></span>.</cite></ref>
* 550,731,776 = 56<sup>5</sup>
* 554,999,445 = 以 10 为基数表示数字长度 9 的[[黑洞數|Kaprekar 常数]]
* 555,555,555 = [[純位數]]
* 574,304,985 = 1<sup>9</sup> + 2<sup>9</sup> + 3<sup>9</sup> + 4<sup>9</sup> + 5<sup>9</sup> + 6<sup>9</sup> + 7<sup>9</sup> + 8<sup>9</sup> + 9<sup>9</sup>{{Hair space}}<ref>{{SloanesRef|A031971}}</ref>
* 575,023,344 = x<sup>x</sup> 在 x=1 处的 14 阶导数<ref>{{SloanesRef|A005727}}</ref>
* 594,823,321 = 24389<sup>2</sup> = 841<sup>3</sup> = 29<sup>6</sup>
* 596,572,387 = 韦德本-埃瑟林顿素数<ref name=":0">{{SloanesRef|A001190|Wedderburn-Etherington numbers|access-date=2016-06-17}}<cite class="citation web cs1" data-ve-ignore="true" id="CITEREFSloane_&quot;A001190&quot;">[[尼爾·斯洛恩|Sloane, N.&nbsp;J.&nbsp;A.]] (ed.). [[oeis:A001190|"Sequence&#x20;A001190&#x20;(Wedderburn-Etherington numbers)"]]. ''The [[整數數列線上大全|On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-06-17</span></span>.</cite></ref>

=== 600,000,000 至 699,999,999 ===

* 601,692,057 = 57<sup>5</sup>
* 612,220,032 = 18<sup>7</sup>
* 617,323,716 = 24846<sup>2</sup>, 回文平方
* 635,318,657 = [[萊昂哈德·歐拉|欧拉]]知道的两个四次方以两种不同方式相加的最小数 ( {{Nowrap|59{{sup|4}} + 158{{sup|4}} {{=}} 133{{sup|4}} + 134{{sup|4}}}} )。
* 644,972,544 = 864<sup>3</sup>, 3-[[光滑數|平滑数]]
* 656,356,768 = 58<sup>5</sup>
* 666,666,666 = [[純位數]]
* 670,617,279 = [[考拉兹猜想|Collatz 猜想]]的 10<sup>9</sup>以下的最高停止时间[[整数]]

=== 700,000,000 至 799,999,999 ===

* 701,408,733 = [[斐波那契数列|斐波那契数]]
* 714,924,299 = 59<sup>5</sup>
* 715,497,037 = 具有 38 个节点的缩减树的数量<ref name="未命名_4-20231105161103"/>
* 715,827,883 =[[瓦格斯塔夫質數|瓦格斯塔夫素数]]， <ref>{{Cite web|title=Sloane's A000979 : Wagstaff primes|url=https://oeis.org/A000979|access-date=2016-06-17|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|archive-date=2010-11-25|archive-url=https://web.archive.org/web/20101125015414/https://oeis.org/A000979|dead-url=no}}</ref>雅各布斯塔尔素数
* 725,594,112 = GF(2) 上的 36 次本原多项式的数量<ref name="未命名_6-20231105161103"/>
* 729,000,000 = 27000<sup>2</sup> = 900<sup>3</sup> = 30<sup>6</sup>
* 742,624,232 = 免费 19 联骨牌数量
* 774,840,978 = 利兰数
* 777,600,000 = 60<sup>5</sup>
* 777,777,777 = [[純位數]]
* 778,483,932 = [[oeis:A000957|Fine Number]]
* 780,291,637 = 马尔可夫素数
* 787,109,376 = 1-[[自守数]]<ref name="automorphic">{{SloanesRef|A003226|Automorphic numbers}}<cite class="citation web cs1" data-ve-ignore="true" id="CITEREFSloane_&quot;A003226&quot;">[[尼爾·斯洛恩|Sloane, N.&nbsp;J.&nbsp;A.]] (ed.). [[oeis:A003226|"Sequence&#x20;A003226&#x20;(Automorphic numbers)"]]. ''The [[整數數列線上大全|On-Line Encyclopedia of Integer Sequences]]''. OEIS Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-04-06</span></span>.</cite></ref>

=== 800,000,000 至 899,999,999 ===

* 815,730,721 = 13<sup>8</sup>
* 815,730,721 = 169<sup>4</sup>
* 835,210,000 = 170<sup>4</sup>
* 837,759,792 = 26 个单元的平行四边形多骨牌数量。 <ref name="未命名_3-20231105161103"/>
* 844,596,301 = 61<sup>5</sup>
* 855,036,081 = 171<sup>4</sup>
* 875,213,056 = 172<sup>4</sup>
* 887,503,681 = 31<sup>6</sup>
* 888,888,888 = [[纯位数]]
* 893,554,688 = 2-[[自守数]]<ref>{{SloanesRef|A030984|2-automorphic numbers|access-date=2021-09-01}}</ref>
* 893,871,739 = 19<sup>7</sup>
* 895,745,041 = 173<sup>4</sup>

=== 900,000,000 至 999,999,999 ===

* 906,150,257 = 波利亚猜想的最小反例
* 916,132,832 = 62<sup>5</sup>
* 923,187,456 = 30384<sup>2</sup> ，最大的无零泛数字平方
* 928,772,650 = 补数相等的 37 珠项链数量（允许翻转） <ref name="未命名-20231105161103"/>
* 929,275,200 = GF(2) 上的 35 次本原多项式的数量<ref name="未命名_6-20231105161103"/>
* 942,060,249 = 30693<sup>2</sup>，回文平方
* 987,654,321 = 最大的无零泛数字
* 992,436,543 = 63<sup>5</sup>
* 997,002,999 = 999<sup>3</sup> ，最大的9位立方
* 999,950,884 = 31622<sup>2</sup> ，最大的九位数平方
* 999,961,560 = 最大的 9 位数[[三角形數|三角数]]和第 44,720 个三角数
* 999,999,937 = 最大的 9 位质数
* 999,999,999 = [[純位數]]

== 参考 ==
{{Reflist}}{{大数}}
[[Category:整数]]