素数の一覧

素数の一覧（そすうのいちらん）では、素数を小さいものから順にリストする。素数は無限に存在するため網羅は不可能であるが、ここでは小さい順に200個の一覧を載せる。

小さい素数のリスト

次の表は、素数を小さいものから順に200個リストしたものである。^[1]^[2]

	1	2	3	4	5	6	7	8	9	10
0	$2$	$3$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$29$
10	$31$	$37$	$41$	$43$	$47$	$53$	$59$	$61$	$67$	$71$
20	$73$	$79$	$83$	$89$	$97$	$101$	$103$	$107$	$109$	$113$
30	$127$	$131$	$137$	$139$	$149$	$151$	$157$	$163$	$167$	$173$
40	$179$	$181$	$191$	$193$	$197$	$199$	$211$	$223$	$227$	$229$
50	$233$	$239$	$241$	$251$	$257$	$263$	$269$	$271$	$277$	$281$
60	$283$	$293$	$307$	$311$	$313$	$317$	$331$	$337$	$347$	$349$
70	$353$	$359$	$367$	$373$	$379$	$383$	$389$	$397$	$401$	$409$
80	$419$	$421$	$431$	$433$	$439$	$443$	$449$	$457$	$461$	$463$
90	$467$	$479$	$487$	$491$	$499$	$503$	$509$	$521$	$523$	$541$

	1	2	3	4	5	6	7	8	9	10
100	$547$	$557$	$563$	$569$	$571$	$577$	$587$	$593$	$599$	$601$
110	$607$	$613$	$617$	$619$	$631$	$641$	$643$	$647$	$653$	$659$
120	$661$	$673$	$677$	$683$	$691$	$701$	$709$	$719$	$727$	$733$
130	$739$	$743$	$751$	$757$	$761$	$769$	$773$	$787$	$797$	$809$
140	$811$	$821$	$823$	$827$	$829$	$839$	$853$	$857$	$859$	$863$
150	$877$	$881$	$883$	$887$	$907$	$911$	$919$	$929$	$937$	$941$
160	$947$	$953$	$967$	$971$	$977$	$983$	$991$	$997$	$1009$	$1013$
170	$1019$	$1021$	$1031$	$1033$	$1039$	$1049$	$1051$	$1061$	$1063$	$1069$
180	$1087$	$1091$	$1093$	$1097$	$1103$	$1109$	$1117$	$1123$	$1129$	$1151$
190	$1153$	$1163$	$1171$	$1181$	$1187$	$1193$	$1201$	$1213$	$1217$	$1223$

ゴールドバッハの予想検証プロジェクトは、 $4 \times 10 18$ 以下のすべての素数（9京5,676兆2,609億0,388万7,607個、つまり約 10¹⁷個）を計算したと報告した^[3]^[4]が、結果は保存されていない。しかしながら、指定された値 $n$ 以下の素数の個数（素数計数関数）を計算するには、実際に素数を数えるより高速な公式が存在する。この公式を使って、 $1023$ 以下に 19垓2,532京0,391兆6,068億0,396万8,923個 (約 2×10²¹個)の素数があると計算された。

また、別の計算によるともしリーマン予想が真であれば、 $1024$ 以下に 184垓3,559京9,767兆3,492億0,086万7,866個(約 2×10²²個) の素数が存在する^[5]。

脚注

[脚注の使い方]

^ Lehmer, D. N. (1982). List of prime numbers from 1 to 10,006,721. 165. Washington D.C.: Carnegie Institution of Washington. OL16553580M
^ オンライン整数列大辞典の数列 A000040
^ Tomás Oliveira e Silva,Goldbach conjecture verification. Retrieved 16 July 2013
^ オンライン整数列大辞典の数列 A080127
^ Jens Franke (2010年7月29日). “Conditional Calculation of pi(10²⁴)”. 2015年2月2日閲覧。

外部リンク

素数のリスト - 国立大学法人大阪教育大学
素数の不思議な性質 - 京都産業大学

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