【数表】500以下の素数の原始根一覧

160912_00

　需要云々は関係なく, ブログという形で残しておきたい, ネットで探して余り見かけないような数表をちょくちょく載せたいと思います.

　第一弾は原始根.

[Contents]

原始根とは
- 原始根の特徴
原始根の一覧
〆

原始根とは

thetheorier.hatenablog.com

　再び書くと長くなるのでこちらを参照ください.

　定義だけは以下に書いておきます.

[定義：原始根]

　素数 $p$ と, $p$ で割り切れない整数 $a$ について, $a$ が $p-1$ に対応するとき, つまり $p-1$ よりも小さな正指数で $a^{e}\equiv 1\pmod p$ という形にならないとき, $a$ は $p$ の原始根と言います.

原始根の特徴

　原始根にはいくつかの性質があります, 自明なものから証明が必要なもの, 推論までいくつか挙げておきます.

　以下, $p$ を奇素数(2以外の素数), $r$ をその原始根とします.

[原始根の数]

　奇素数 $p$ の原始根は $1, 2, \dots ,p$ の中に $\varphi(\varphi(p))=\varphi(p-1)$ 個だけ存在する.

[推論]

　素数 $p$ とその原始根 $r$ について,

$\Bigl|\text{Ind}_{r}\frac{p-1}{2} - \text{Ind}_{r}\frac{p+1}{2}\Bigr| = \frac{p-1}{2}$

, 特に

$\text{Ind}_{r}(1)=0$
$\text{Ind}_{r}(p-1)=\frac{p-1}{2}$

　特に…については自明ですね.

　また平方剰余を用いて原始根を判定, そして芋づる式に他の原始根を求める方法もあります, いづれ説明したいと思います.

原始根の一覧

　500以下の奇素数, p=3から499までの原始根の一覧を紹介します, 計算間違いがあったら指摘ください.

p=3～97

p=3	1個
2

p=5	2個
2,3

p=7	2個
3,5

p=11	4個
2,6,7,8

p=13	4個
2,6,7,11

p=17	8個
3,5,6,7,10,11,12,14

p=19	6個
2,3,10,13,14,15

p=23	10個
5,7,10,11,14,15,17,19,20,21

p=29	12個
2,3,8,10,11,14,15,18,19,21,26,27

p=31	8個
3,11,12,13,17,21,22,24

p=37	12個
2,5,13,15,17,18,19,20,22,24,32,35

p=41	16個
6,7,11,12,13,15,17,19,22,24,26,28,29,30,34,35

p=43	12個
3,5,12,18,19,20,26,28,29,30,33,34

p=47	22個
5,10,11,13,15,19,20,22,23,26,29,30,31,33,35,38,39,40,41,43,44,45

p=53	24個
2,3,5,8,12,14,18,19,20,21,22,26,27,31,32,33,34,35,39,41,45,48,50,51

p=59	28個
2,6,8,10,11,13,14,18,23,24,30,31,32,33,34,37,38,39,40,42,43,44,47,50,52,54,55,56

p=61	16個
2,6,7,10,17,18,26,30,31,35,43,44,51,54,55,59

p=67	20個
2,7,11,12,13,18,20,28,31,32,34,41,44,46,48,50,51,57,61,63

p=71	24個
7,11,13,21,22,28,31,33,35,42,44,47,52,53,55,56,59,61,62,63,65,67,68,69

p=73	24個
5,11,13,14,15,20,26,28,29,31,33,34,39,40,42,44,45,47,53,58,59,60,62,68

p=79	24個
3,6,7,28,29,30,34,35,37,39,43,47,48,53,54,59,60,63,66,68,70,74,75,77

p=83	40個
2,5,6,8,13,14,15,18,19,20,22,24,32,34,35,39,42,43,45,46,47,50,52,53,54,55,56,57,58,60,62,66,67,71,72,73,74,76,79,80

p=89	40個
3,6,7,13,14,15,19,23,24,26,27,28,29,30,31,33,35,38,41,43,46,48,51,54,56,58,59,60,61,62,63,65,66,70,74,75,76,82,83,86

p=97	32個
5,7,10,13,14,15,17,21,23,26,29,37,38,39,40,41,56,57,58,59,60,68,71,74,76,80,82,83,84,87,90,92

p=101～199

p=101	40個
2,3,7,8,11,12,15,18,26,27,28,29,34,35,38,40,42,46,48,50,51,53,55,59,61,63,66,67,72,73,74,75,83,86,89,90,93,94,98,99

p=103	32個
5,6,11,12,20,21,35,40,43,44,45,48,51,53,54,62,65,67,70,71,74,75,77,78,84,85,86,87,88,96,99,101

p=107	52個
2,5,6,7,8,15,17,18,20,21,22,24,26,28,31,32,38,43,45,46,50,51,54,55,58,59,60,63,65,66,67,68,70,71,72,73,74,77,78,80,82,84,88,91,93,94,95,96,97,98,103,104

p=109	36個
6,10,11,13,14,18,24,30,37,39,40,42,44,47,50,51,52,53,56,57,58,59,62,65,67,69,70,72,79,85,91,95,96,98,99,103

p=113	48個
3,5,6,10,12,17,19,20,21,23,24,27,29,33,34,37,38,39,43,45,46,47,54,55,58,59,66,67,68,70,74,75,76,79,80,84,86,89,90,92,93,94,96,101,103,107,108,110

p=127	36個
3,6,7,12,14,23,29,39,43,45,46,48,53,55,56,57,58,65,67,78,83,85,86,91,92,93,96,97,101,106,109,110,112,114,116,118

p=131	48個
2,6,8,10,14,17,22,23,26,29,30,31,37,40,50,54,56,57,66,67,72,76,82,83,85,87,88,90,93,95,96,97,98,103,104,106,110,111,115,116,118,119,120,122,124,126,127,128

p=137	64個
3,5,6,12,13,20,21,23,24,26,27,29,31,33,35,40,42,43,45,46,47,48,51,52,53,54,55,57,58,62,66,67,70,71,75,79,80,82,83,84,85,86,89,90,91,92,94,95,97,102,104,106,108,110,111,113,114,116,117,124,125,131,132,134

p=139	44個
2,3,12,15,17,18,19,21,22,26,32,40,50,53,56,58,61,68,70,72,73,85,88,90,92,93,98,101,102,104,108,109,110,111,114,115,119,123,126,128,130,132,134,135

p=149	72個
2,3,8,10,11,12,13,14,15,18,21,23,27,32,34,38,40,41,43,48,50,51,52,55,56,57,58,59,60,62,65,66,70,71,72,74,75,77,78,79,83,84,87,89,90,91,92,93,94,97,98,99,101,106,108,109,111,115,117,122,126,128,131,134,135,136,137,138,139,141,146,147

p=151	40個
6,7,12,13,14,15,30,35,48,51,52,54,56,61,63,71,77,82,89,93,96,102,104,106,108,109,111,112,114,115,117,120,126,129,130,133,134,140,141,146

p=157	48個
5,6,15,18,20,21,24,26,34,38,43,53,55,60,61,62,63,66,69,70,72,73,74,77,80,83,84,85,87,88,91,94,95,96,97,102,104,114,119,123,131,133,136,137,139,142,151,152

p=163	54個
2,3,7,11,12,18,19,20,29,32,42,44,45,50,52,63,66,67,68,70,72,73,75,76,79,80,82,89,92,94,101,103,106,107,108,109,112,114,116,117,120,122,124,128,129,130,137,139,147,148,149,153,154,159

p=167	82個
5,10,13,15,17,20,23,26,30,34,35,37,39,40,41,43,45,46,51,52,53,55,59,60,67,68,69,70,71,73,74,78,79,80,82,83,86,90,91,92,95,101,102,103,104,105,106,109,110,111,113,117,118,119,120,123,125,129,131,134,135,136,138,139,140,142,143,145,146,148,149,151,153,155,156,158,159,160,161,163,164,165

p=173	84個
2,3,5,7,8,11,12,17,18,19,20,26,27,28,30,32,39,42,44,45,46,48,50,53,58,59,61,62,63,65,66,68,69,70,71,72,74,75,76,79,82,86,87,91,94,97,98,99,101,102,103,104,105,107,108,110,111,112,114,115,120,123,125,127,128,129,131,134,141,143,145,146,147,153,154,155,156,161,162,165,166,168,170,171

p=179	88個
2,6,7,8,10,11,18,21,23,24,26,28,30,32,33,34,35,37,38,40,41,44,50,53,54,55,58,62,63,69,71,72,73,78,79,84,86,90,91,92,94,96,97,98,99,102,103,104,105,109,111,112,113,114,115,118,119,120,122,123,127,128,130,131,132,133,134,136,137,140,143,148,150,152,154,157,159,160,162,163,164,165,166,167,170,174,175,176

p=181	48個
2,10,18,21,23,24,28,41,47,50,53,54,57,58,63,66,69,76,77,78,83,84,85,90,91,96,97,98,103,104,105,112,115,118,123,124,127,128,131,134,140,153,157,158,160,163,171,179

p=191	72個
19,21,22,28,29,33,35,42,44,47,53,56,57,58,61,62,63,71,73,74,76,83,87,88,89,91,93,94,95,99,101,105,106,110,111,112,113,114,116,119,123,124,126,127,131,132,137,140,141,143,145,146,148,151,157,164,165,167,168,171,173,174,175,176,178,179,181,182,183,187,188,189

p=193	64個
5,10,15,17,19,22,26,30,34,37,38,40,41,44,45,47,51,52,53,57,58,61,66,70,73,77,78,79,80,82,90,91,102,103,111,113,114,115,116,120,123,127,132,135,136,140,141,142,146,148,149,152,153,155,156,159,163,167,171,174,176,178,183,188

p=197	84個
2,3,5,8,11,12,13,17,18,21,27,30,31,32,35,38,44,45,46,48,50,52,56,57,58,66,67,71,72,73,74,75,78,79,80,82,86,89,91,94,95,98,99,102,103,106,108,111,115,117,118,119,122,123,124,125,126,130,131,139,140,141,145,147,149,151,152,153,159,162,165,166,167,170,176,179,180,184,185,186,189,192,194,195

p=199	60個
3,6,15,22,30,34,38,39,41,44,48,54,68,69,71,73,75,77,84,87,95,97,99,105,108,110,113,118,119,120,127,129,133,134,142,143,146,148,149,150,152,153,154,163,164,166,167,168,170,173,176,179,183,185,186,189,190,192,195,197

p=211～293

p=211	48個
2,3,7,17,22,29,35,39,41,48,57,72,75,85,91,92,106,108,112,116,118,127,130,131,133,141,142,145,149,152,155,158,159,160,162,164,165,166,167,174,175,181,187,191,195,202,205,207

p=223	72個
3,5,6,10,11,12,20,21,22,23,24,35,42,44,45,46,48,51,57,61,67,70,71,75,77,79,80,84,85,88,90,92,93,96,97,99,102,107,113,114,117,122,123,129,134,137,140,142,145,147,149,150,151,154,158,160,161,165,168,170,173,176,180,185,186,187,192,194,198,204,205,214

p=227	112個
2,5,6,8,13,14,15,17,18,20,22,24,31,32,35,37,38,39,41,42,45,46,50,51,52,54,55,56,58,60,61,66,67,68,72,80,83,86,88,91,93,94,95,96,98,105,106,107,111,114,115,117,118,119,123,124,125,126,127,128,130,135,137,138,140,142,143,145,146,148,149,150,151,152,153,154,156,157,158,162,163,164,165,168,170,174,178,179,180,183,184,187,191,193,194,197,198,199,200,201,202,204,206,208,211,215,216,217,218,220,223,224

p=229	72個
6,7,10,23,24,28,29,31,35,38,39,40,41,47,50,59,63,65,66,67,69,72,73,74,77,79,87,90,92,96,98,102,105,110,112,113,116,117,119,124,127,131,133,137,139,142,150,152,155,156,157,160,162,163,164,166,170,179,182,188,189,190,191,194,198,200,201,205,206,219,222,223

p=233	112個
3,5,6,10,11,17,20,21,22,24,27,34,35,39,40,41,42,43,44,45,47,48,53,54,57,59,61,65,67,68,69,70,73,75,77,78,79,80,82,83,84,86,87,88,90,93,94,95,96,99,103,106,108,111,114,115,118,119,122,125,127,130,134,137,138,139,140,143,145,146,147,149,150,151,153,154,155,156,158,160,163,164,165,166,168,172,174,176,179,180,185,186,188,189,190,191,192,193,194,198,199,206,209,211,212,213,216,222,223,227,228,230

p=239	96個
7,13,14,19,21,26,35,37,39,41,42,43,46,47,53,56,57,59,63,65,69,70,74,77,78,79,82,84,86,89,92,94,95,97,103,104,105,106,112,114,115,117,118,119,123,126,129,130,131,137,140,143,146,148,149,151,152,154,156,158,159,167,171,173,175,177,178,179,181,184,185,189,190,191,194,205,206,207,208,209,210,212,214,219,221,222,223,224,227,228,230,231,234,235,236,237

p=241	64個
7,13,14,31,34,35,37,39,42,46,51,52,55,56,62,66,68,69,70,71,74,78,84,86,92,95,99,104,109,110,112,114,127,129,131,132,137,142,146,149,155,157,163,167,170,171,172,173,175,179,185,186,189,190,195,199,202,204,206,207,210,227,228,234

p=251	100個
6,11,14,18,19,24,26,29,30,33,34,37,42,43,44,46,53,54,55,56,57,59,61,62,70,71,72,76,77,78,82,87,90,95,96,97,98,99,104,107,109,111,116,120,127,129,130,132,133,134,136,137,139,141,143,145,146,148,150,158,159,162,163,165,166,167,168,170,172,176,177,178,183,184,185,186,191,193,199,202,203,206,210,212,213,215,216,220,223,224,228,229,230,234,236,238,239,242,244,248

p=257

128個

3,5,6,7,10,12,14,19,20,24,27,28,33,37,38,39,40,41,43,45,47,48,51,53,54,55,56,63,65,66,69,71,74,75,76,77,78,80,82,83,85,86,87,90,91,93,94,96,97,101,102,103,105,106,107,108,109,110,112,115,119,125,126,127,130,131,132,138,142,145,147,148,149,150,151,152,154,155,156,160,161,163,164,166,167,170,171,172,174,175,177,179,180,181,182,183,186,188,191,192,194,201,202,203,204,206,209,210,212,214,216,217,218,219,220,224,229,230,233,237,238,243,245,247,250,251,252,254

p=263

130個

5,7,10,14,15,19,20,21,28,29,30,38,40,41,42,45,47,53,55,56,57,58,59,60,63,65,67,71,73,76,77,79,80,82,84,85,87,90,91,94,97,101,106,107,110,112,113,114,115,116,118,119,120,123,125,126,127,130,131,134,135,139,141,142,146,152,154,155,158,159,160,161,163,164,165,167,168,170,171,174,175,177,180,182,185,188,189,191,193,194,195,197,199,201,202,209,211,212,213,214,215,217,219,220,224,226,227,228,229,230,231,232,236,237,238,239,240,241,245,246,247,250,251,252,254,255,257,259,260,261

p=269

132個

2,3,7,8,10,12,15,17,18,19,22,26,27,28,29,31,32,33,35,39,40,42,46,48,50,59,60,63,68,69,71,72,74,75,76,77,83,85,86,88,90,91,94,95,98,101,102,104,106,107,108,109,110,111,112,113,114,116,122,123,124,128,129,130,132,134,135,137,139,140,141,145,146,147,153,155,156,157,158,159,160,161,162,163,165,167,168,171,174,175,178,179,181,183,184,186,192,193,194,195,197,198,200,201,206,209,210,219,221,223,227,229,230,234,236,237,238,240,241,242,243,247,250,251,252,254,257,259,261,262,266,267

p=271	72個
6,15,21,26,38,42,43,46,48,51,52,58,59,66,71,73,75,76,91,92,94,95,96,97,101,107,108,109,116,118,120,133,135,137,142,143,147,149,150,159,161,168,172,182,186,189,193,197,201,203,204,208,209,210,215,218,221,222,226,231,234,235,249,251,253,254,255,257,260,264,267,269

p=277	88個
5,6,11,14,17,18,20,24,31,43,44,45,46,50,53,56,58,65,68,72,77,78,80,93,94,96,97,98,99,101,103,105,107,110,111,114,115,119,124,126,127,134,135,137,140,142,143,150,151,153,158,162,163,166,167,170,172,174,176,178,179,180,181,183,184,197,199,200,205,209,212,219,221,224,227,231,232,233,234,246,253,257,259,260,263,266,271,272

p=281	96個
3,11,12,13,15,19,21,22,23,24,26,27,30,41,42,44,46,48,51,52,54,55,71,74,75,76,82,83,84,87,91,94,95,96,97,103,104,105,107,108,110,115,117,120,122,127,131,133,148,150,154,159,161,164,166,171,173,174,176,177,178,184,185,186,187,190,194,197,198,199,205,206,207,210,226,227,229,230,233,235,237,239,240,251,254,255,257,258,259,260,262,266,268,269,270,278

p=283	92個
3,5,12,14,17,18,20,22,26,31,35,37,46,47,48,50,55,56,65,68,69,72,75,80,82,87,88,98,104,107,109,114,118,119,123,124,126,133,139,140,145,146,147,148,153,154,162,166,170,171,173,178,180,182,183,184,186,187,188,189,190,191,192,193,194,198,200,202,206,209,210,213,220,221,224,226,231,234,242,243,247,249,255,258,259,260,270,272,273,274,276,277

p=293

144個

2,3,5,7,8,11,12,13,18,19,20,23,27,28,29,30,32,34,41,42,44,45,47,48,50,51,52,62,63,66,70,72,74,75,76,78,79,80,85,86,89,92,93,98,99,101,103,105,106,108,110,111,112,113,114,116,117,118,119,120,122,125,127,128,129,130,131,134,136,139,142,146,147,151,154,157,159,162,163,164,165,166,168,171,173,174,175,176,177,179,180,181,182,183,185,187,188,190,192,194,195,200,201,204,207,208,213,214,215,217,218,219,221,223,227,230,231,241,242,243,245,246,248,249,251,252,259,261,263,264,265,266,270,273,274,275,280,281,282,285,286,288,290,291

p=307～397

p=307	96個
5,13,14,21,22,23,29,30,31,43,45,47,50,52,55,56,59,61,67,73,74,75,78,80,82,84,85,88,92,95,98,106,111,116,117,120,123,124,126,130,131,132,137,138,142,143,147,151,157,159,161,166,172,173,174,178,180,185,186,188,189,195,197,198,200,203,207,208,213,217,218,220,221,224,236,238,241,242,244,245,247,249,258,263,265,266,267,268,270,279,281,282,292,296,297,300

p=311

120個

17,19,22,23,29,31,33,34,37,38,43,44,55,57,58,59,62,66,69,71,74,76,82,85,88,92,93,97,99,101,102,103,110,111,114,115,118,119,122,123,124,129,131,132,133,136,138,145,148,149,151,152,153,154,155,161,164,167,170,172,174,176,177,181,183,184,186,191,194,199,202,203,204,205,207,211,213,215,217,221,227,230,231,232,233,236,238,239,241,244,246,247,248,251,255,257,258,261,263,266,269,271,272,276,281,283,284,285,286,290,295,297,299,301,302,303,306,307,308,309

p=313	96個
10,14,15,17,20,21,28,31,34,37,41,45,46,47,55,59,60,62,63,65,67,69,74,77,80,84,86,89,90,91,92,94,101,102,106,109,110,112,120,122,123,126,127,130,146,149,153,154,159,160,164,167,183,186,187,190,191,193,201,203,204,207,211,212,219,221,222,223,224,227,229,233,236,239,244,246,248,250,251,253,254,258,266,267,268,272,276,279,282,285,292,293,296,298,299,303

p=317

156個

2,3,5,8,12,13,14,17,18,19,20,21,22,27,29,30,32,33,35,41,45,46,47,48,50,52,55,56,62,68,69,71,72,74,75,76,78,80,84,86,88,91,93,97,98,102,106,107,108,109,111,115,116,117,118,119,120,122,125,126,127,128,129,130,132,133,134,137,139,140,143,146,147,151,153,154,155,158,159,162,163,164,166,170,171,174,177,178,180,183,184,185,187,188,189,190,191,192,195,197,198,199,200,201,202,206,208,209,210,211,215,219,220,224,226,229,231,233,237,239,241,242,243,245,246,248,249,255,261,262,265,267,269,270,271,272,276,282,284,285,287,288,290,295,296,297,298,299,300,303,304,305,309,312,314,315

p=331	80個
3,11,28,29,35,37,40,41,42,44,50,55,59,60,63,66,86,90,93,97,98,99,101,107,129,134,135,136,137,140,147,148,152,158,160,170,175,182,190,192,201,204,208,209,210,217,218,221,222,227,228,237,240,244,249,250,254,255,260,262,273,277,278,285,286,288,292,295,301,305,306,307,310,311,312,314,317,322,325,326

p=337	96個
10,15,19,20,22,23,29,31,33,34,44,45,46,51,53,60,61,67,68,70,71,73,80,83,87,89,90,93,99,101,106,109,114,116,118,120,124,130,132,134,139,143,151,152,154,160,161,166,171,176,177,183,185,186,194,198,203,205,207,213,217,219,221,223,228,231,236,238,244,247,248,250,254,257,264,266,267,269,270,276,277,284,286,291,292,293,303,304,306,308,314,315,317,318,322,327

p=347

172個

2,5,6,7,8,15,17,18,19,20,21,22,23,24,26,28,32,37,41,45,47,50,51,54,55,57,58,60,62,63,65,66,68,69,70,72,76,77,78,79,80,84,86,88,91,92,96,97,98,101,103,104,106,111,112,118,122,123,125,128,134,135,139,141,142,145,146,148,150,151,153,155,162,163,164,165,166,170,171,174,175,178,179,180,186,187,188,189,190,191,193,195,198,200,203,204,207,209,210,211,214,215,216,217,218,220,221,223,226,227,228,230,231,232,233,234,237,238,239,240,242,245,247,248,252,253,254,257,258,260,262,264,265,266,272,273,274,276,280,283,286,288,291,294,295,298,299,301,303,304,305,307,308,309,311,312,313,314,316,317,318,320,322,331,333,334,335,336,337,338,343,344

p=349

112個

2,7,13,18,30,32,33,34,40,43,44,46,50,54,55,59,62,63,71,72,74,82,84,89,90,96,97,99,105,107,112,113,114,117,119,120,128,129,132,134,137,138,140,141,149,150,152,154,156,159,161,165,166,172,173,174,175,176,177,183,184,188,190,193,195,197,199,200,208,209,211,212,215,217,220,221,229,230,232,235,236,237,242,244,250,252,253,259,260,265,267,275,277,278,286,287,290,294,295,299,303,305,306,309,315,316,317,319,331,336,342,347

p=353

160個

3,5,12,13,14,20,24,26,27,28,31,33,37,40,45,48,51,52,53,54,55,56,57,62,63,66,69,71,74,75,77,79,80,85,87,89,90,95,96,102,103,104,105,107,108,110,112,114,115,117,118,119,123,124,125,126,129,132,133,134,138,139,141,142,143,145,147,148,149,150,151,154,158,160,161,163,170,173,174,175,178,179,180,183,190,192,193,195,199,202,203,204,205,206,208,210,211,212,214,215,219,220,221,224,227,228,229,230,234,235,236,238,239,241,243,245,246,248,249,250,251,257,258,263,264,266,268,273,274,276,278,279,282,284,287,290,291,296,297,298,299,300,301,302,305,308,313,316,320,322,325,326,327,329,333,339,340,341,348,350

p=359

178個

7,13,14,19,21,26,28,29,31,35,38,39,42,43,52,53,56,57,58,59,61,62,63,65,67,70,71,76,77,78,83,84,86,87,89,93,95,97,103,104,105,106,109,112,113,114,116,117,118,119,122,124,126,129,130,134,137,139,140,142,143,145,152,154,155,156,157,159,161,163,166,167,168,171,172,174,175,177,178,179,183,186,189,190,194,195,197,199,201,206,208,209,210,211,212,213,215,218,221,223,224,226,227,228,231,232,234,236,238,239,244,248,249,251,252,257,258,259,260,261,263,265,267,268,269,271,274,277,278,279,280,284,285,286,287,290,291,293,295,299,304,305,308,309,310,311,312,313,314,315,318,319,322,323,325,326,327,329,332,334,335,336,337,339,341,342,343,344,347,348,349,350,351,353,354,355,356,357

p=367

120個

6,10,11,12,17,19,20,22,34,39,42,43,48,54,58,65,69,70,71,76,77,78,79,80,88,90,93,96,97,99,103,108,111,115,116,119,123,127,130,131,133,136,139,140,143,150,152,153,154,155,157,159,160,165,171,172,176,179,180,183,185,186,193,194,197,198,201,205,206,218,219,221,223,238,239,241,246,249,250,254,255,257,263,265,267,269,272,273,275,276,278,282,285,294,300,301,305,306,307,310,312,314,316,317,326,330,331,334,335,336,337,339,341,344,349,351,353,354,363,365

p=373

120個

2,5,6,11,14,15,24,26,32,34,35,42,43,44,47,53,54,57,60,61,62,65,72,76,77,78,79,80,82,85,92,98,99,102,105,110,118,127,128,131,132,135,141,143,149,150,151,155,159,162,166,168,171,172,174,178,180,182,183,186,187,190,191,193,195,199,201,202,205,207,211,214,218,222,223,224,230,232,238,241,242,245,246,255,263,268,271,274,275,281,288,291,293,294,295,296,297,301,308,311,312,313,316,319,320,326,329,330,331,338,339,341,347,349,358,359,362,367,368,371

p=379	108個
2,3,7,10,12,13,15,17,18,28,31,32,35,38,42,43,46,47,50,53,55,60,65,66,71,72,74,75,78,82,89,90,98,99,102,109,113,116,117,122,123,131,134,152,153,154,155,158,160,161,168,172,175,176,188,190,192,201,206,208,209,210,215,223,230,231,233,235,236,238,243,247,249,250,252,253,259,261,265,269,273,274,275,276,278,279,282,283,284,287,291,298,299,317,321,323,325,330,334,345,353,357,358,359,360,363,370,375

p=383

190個

5,10,11,13,15,20,22,26,30,33,35,37,39,40,41,44,45,47,52,53,59,60,61,66,70,74,77,78,79,80,82,83,85,88,89,90,91,94,95,97,99,104,105,106,107,109,111,115,117,118,120,122,123,125,127,131,132,135,140,141,145,148,151,154,155,156,157,158,159,160,163,164,166,167,170,176,177,178,179,180,181,182,183,187,188,190,191,194,197,198,199,208,209,210,211,212,214,215,218,221,222,230,231,233,234,236,237,239,240,241,244,245,246,247,249,250,253,254,255,257,259,262,264,267,269,270,271,273,275,280,281,282,283,285,287,290,291,296,297,299,302,307,308,310,311,312,314,315,316,318,319,320,321,325,326,327,328,329,332,333,334,335,337,340,341,345,347,349,351,352,354,355,356,358,359,360,362,364,365,366,367,369,371,374,375,376,377,379,380,381

p=389

192個

2,3,8,10,12,14,15,18,21,22,23,26,27,29,31,32,33,34,37,38,39,40,43,47,48,50,51,53,56,57,60,61,70,71,72,75,82,83,84,88,89,90,92,98,101,103,104,105,107,108,109,110,116,118,123,124,126,128,130,131,132,134,135,136,138,139,145,146,147,148,149,151,152,154,155,156,158,160,161,162,163,165,167,170,172,174,177,182,185,186,188,189,190,191,192,194,195,197,198,199,200,201,203,204,207,212,215,217,219,222,224,226,227,228,229,231,233,234,235,237,238,240,241,242,243,244,250,251,253,254,255,257,258,259,261,263,265,266,271,273,279,280,281,282,284,285,286,288,291,297,299,300,301,305,306,307,314,317,318,319,328,329,332,333,336,338,339,341,342,346,349,350,351,352,355,356,357,358,360,362,363,366,367,368,371,374,375,377,379,381,386,387

p=397

120個

5,6,7,13,18,20,21,22,24,28,38,39,45,46,50,51,52,58,59,61,66,72,74,77,80,84,89,94,98,101,109,112,114,133,134,135,138,139,143,146,150,152,155,156,158,159,161,162,164,165,170,174,175,180,182,186,187,189,193,197,200,204,208,210,211,215,217,222,223,227,232,233,235,236,238,239,241,242,245,247,251,254,258,259,262,263,264,283,285,288,296,299,303,308,313,317,320,323,325,331,336,338,339,345,346,347,351,352,358,359,369,373,375,376,377,379,384,390,391,392

p=401～499

p=401

160個

3,6,12,13,15,17,19,21,23,24,27,31,34,37,38,42,46,52,53,54,59,60,61,62,65,66,67,71,74,75,79,85,87,91,92,95,96,97,101,104,105,106,107,115,117,118,120,122,123,124,127,129,130,131,132,134,135,136,137,139,141,143,150,152,161,163,165,167,168,170,174,182,184,185,187,190,191,192,193,194,207,208,209,210,211,214,216,217,219,227,231,233,234,236,238,240,249,251,258,260,262,264,265,266,267,269,270,271,272,274,277,278,279,281,283,284,286,294,295,296,297,300,304,305,306,309,310,314,316,322,326,327,330,334,335,336,339,340,341,342,347,348,349,355,359,363,364,367,370,374,377,378,380,382,384,386,388,389,395,398

p=409

128個

21,22,26,28,29,33,35,37,39,42,44,47,52,56,57,62,67,73,74,76,86,87,93,97,99,105,107,110,113,116,118,122,124,126,127,129,130,132,140,141,145,149,156,157,158,165,168,171,172,173,174,175,176,177,181,185,187,188,189,190,195,198,199,201,208,210,211,214,219,220,221,222,224,228,232,233,234,235,236,237,238,241,244,251,252,253,260,264,268,269,277,279,280,282,283,285,287,291,293,296,299,302,304,310,312,316,322,323,333,335,336,342,347,352,353,357,362,365,367,370,372,374,376,380,381,383,387,388

p=419

180個

2,6,8,10,11,14,17,18,19,24,26,30,31,32,33,42,44,46,50,51,53,54,55,56,57,58,61,67,68,70,72,74,77,78,82,83,86,93,94,95,96,98,99,101,103,104,109,118,120,124,126,127,128,130,132,133,138,143,146,150,153,155,158,159,160,162,163,165,167,168,174,176,179,181,182,183,184,193,194,200,201,210,212,213,214,216,217,221,222,223,224,227,228,229,230,231,232,233,234,239,241,242,244,246,247,249,253,255,258,262,263,265,268,270,271,272,274,275,277,278,279,282,285,288,294,296,297,298,302,303,304,307,308,309,311,313,314,319,322,327,328,331,332,335,338,339,340,344,346,353,354,355,356,357,367,371,374,376,378,380,381,382,383,384,385,390,391,392,394,396,397,398,399,403,404,407,410,414,415,416

p=421	96個
2,14,18,22,23,24,30,39,40,41,43,50,53,54,57,65,66,71,72,76,83,87,88,90,96,98,102,116,117,134,136,141,143,145,150,154,160,168,177,183,185,186,193,194,200,208,209,210,211,212,213,221,227,228,235,236,238,244,253,261,267,271,276,278,280,285,287,304,305,319,323,325,331,333,334,338,345,349,350,355,356,364,367,368,371,378,380,381,382,391,397,398,399,403,407,419

p=431

168個

7,13,14,17,21,28,31,34,35,37,39,42,43,51,52,56,62,63,65,67,68,70,71,73,74,77,78,79,83,84,85,86,89,93,102,103,104,105,111,112,113,117,124,126,127,129,130,131,134,136,137,140,142,146,148,153,154,155,156,158,161,166,167,168,170,172,178,181,185,187,189,191,193,195,199,201,203,204,206,208,210,213,219,222,224,226,231,233,234,235,237,241,247,248,249,251,252,254,255,257,258,260,262,267,268,271,272,274,279,280,281,284,292,293,296,299,306,308,309,310,311,312,313,316,317,322,325,331,332,333,334,339,340,341,343,344,349,351,355,356,362,365,370,371,372,373,374,378,381,382,385,386,387,390,391,393,398,401,402,406,408,409,411,412,416,420,421,426

p=433

144個

5,7,10,14,15,19,20,23,28,29,30,31,38,40,46,47,55,56,57,58,60,61,62,63,65,71,76,80,83,85,87,92,93,94,101,107,110,112,113,114,116,120,122,124,126,129,130,135,142,149,152,160,163,166,170,173,174,175,181,184,185,186,188,189,193,201,202,205,207,209,213,214,219,220,224,226,228,231,232,240,244,245,247,248,249,252,258,259,260,263,267,270,273,281,284,291,298,303,304,307,309,311,313,317,319,320,321,323,326,332,339,340,341,346,348,350,353,357,362,368,370,371,372,373,375,376,377,378,386,387,393,395,402,403,404,405,410,413,414,418,419,423,426,428

p=439

144個

15,17,23,30,31,33,34,37,39,41,43,46,57,59,60,62,66,67,68,74,75,78,79,82,85,86,87,89,92,97,101,105,107,114,118,119,120,124,131,132,134,135,136,148,150,153,155,156,158,159,161,163,164,170,173,174,178,181,184,185,193,194,197,202,205,207,210,213,214,217,227,228,231,235,236,238,239,240,241,248,249,253,257,259,262,263,264,270,272,273,279,285,287,296,297,299,300,301,306,310,312,316,318,322,323,326,328,333,335,337,339,340,344,346,348,349,351,356,359,362,363,368,369,370,381,386,387,388,389,394,395,399,401,404,410,413,414,417,419,420,426,428,429,434

p=443

192個

2,5,6,7,8,11,19,20,21,23,24,26,28,29,31,32,33,43,44,45,50,53,54,57,69,70,72,74,76,78,80,82,83,84,85,91,92,93,94,97,98,99,101,102,110,112,116,118,122,124,125,127,128,129,132,134,135,136,142,143,150,154,157,158,159,162,171,172,175,178,179,180,185,187,189,190,193,199,200,206,207,210,211,212,214,216,219,222,223,226,228,230,235,239,240,241,242,245,246,247,249,251,252,257,260,261,262,266,269,273,275,276,277,278,279,280,282,283,287,288,290,291,292,294,295,296,297,298,299,302,303,304,305,306,310,312,313,317,322,323,326,329,330,332,334,335,336,337,338,340,343,348,353,354,355,357,362,364,366,368,372,375,377,379,381,382,385,388,391,392,394,395,396,397,401,402,403,404,406,407,413,416,418,421,426,427,429,431,433,434,439,440

p=449

192個

3,6,12,13,15,17,19,21,26,27,29,30,31,33,34,38,42,43,47,48,54,60,62,65,66,68,69,73,74,75,76,83,85,86,91,94,96,103,104,105,107,109,113,116,117,119,120,123,124,130,132,133,135,136,138,139,142,143,145,146,147,148,149,150,151,152,153,157,158,159,163,165,166,168,170,171,172,173,177,179,183,185,187,189,190,192,201,206,208,210,211,214,216,217,218,223,226,231,232,233,235,238,239,241,243,248,257,259,260,262,264,266,270,272,276,277,278,279,281,283,284,286,290,291,292,296,297,298,299,300,301,302,303,304,306,307,310,311,313,314,316,317,319,325,326,329,330,332,333,336,340,342,344,345,346,353,355,358,363,364,366,373,374,375,376,380,381,383,384,387,389,395,401,402,406,407,411,415,416,418,419,420,422,423,428,430,432,434,436,437,443,446

p=457

144個

13,15,23,26,30,31,33,35,39,41,45,46,52,53,59,60,61,62,66,69,71,77,78,82,89,90,92,95,97,99,101,103,104,106,118,120,122,123,124,129,132,138,140,142,145,149,154,156,159,164,167,173,177,178,179,180,181,184,190,193,194,198,199,202,206,208,209,211,212,213,221,222,235,236,244,245,246,248,249,251,255,258,259,263,264,267,273,276,277,278,279,280,284,290,293,298,301,303,308,312,315,317,319,325,328,333,334,335,337,339,351,353,354,356,358,360,362,365,367,368,375,379,380,386,388,391,395,396,397,398,404,405,411,412,416,418,422,424,426,427,431,434,442,444

p=461

176個

2,3,7,8,10,11,12,15,18,27,28,29,31,34,35,40,42,44,46,47,50,51,52,55,63,65,66,69,78,79,82,83,90,98,99,101,106,112,116,117,118,119,122,123,127,128,131,133,135,136,140,147,148,149,152,154,155,159,160,161,168,170,173,174,176,177,178,183,184,185,187,190,192,194,197,200,204,206,208,210,214,219,220,221,222,226,228,230,231,233,235,239,240,241,242,247,251,253,255,257,261,264,267,269,271,274,276,277,278,283,284,285,287,288,291,293,300,301,302,306,307,309,312,313,314,321,325,326,328,330,333,334,338,339,342,343,344,345,349,355,360,362,363,371,378,379,382,383,392,395,396,398,406,409,410,411,414,415,417,419,421,426,427,430,432,433,434,443,446,449,450,451,453,454,458,459

p=463

120個

3,5,11,19,20,24,26,28,37,40,41,45,46,48,53,54,63,75,76,85,88,92,102,104,108,112,119,127,137,141,142,147,151,152,157,160,164,165,166,171,174,175,176,183,192,195,198,199,202,203,204,207,208,210,214,215,217,223,224,227,231,241,243,245,250,252,257,258,275,278,282,290,291,295,296,301,307,309,310,323,325,327,328,332,333,342,347,348,349,350,353,354,360,365,372,374,382,384,390,391,394,396,401,402,403,404,413,420,421,428,431,432,433,434,438,446,447,454,459,461

p=467

232個

2,5,6,8,11,14,15,18,19,20,24,26,29,31,32,33,34,35,37,42,44,45,46,50,54,56,57,60,61,65,67,72,73,76,77,78,79,80,82,85,86,87,93,94,96,98,99,101,102,103,104,105,106,107,110,111,115,116,118,124,125,126,128,131,132,133,135,136,138,140,142,143,148,150,162,166,167,168,171,176,178,180,181,182,183,184,187,190,191,194,195,197,200,201,203,205,211,215,216,217,218,219,224,226,228,231,234,235,237,238,240,242,244,245,246,247,253,254,255,257,258,259,260,261,263,265,268,269,271,274,275,278,279,281,282,288,290,292,293,294,295,297,298,302,303,304,306,307,308,309,310,311,312,313,314,315,316,318,320,321,322,323,326,328,330,333,337,338,340,344,345,346,347,348,350,353,354,355,358,359,367,370,372,375,376,377,378,379,383,384,386,392,393,396,397,398,399,401,403,404,405,408,409,412,414,415,416,418,419,420,424,426,427,428,429,431,437,439,440,442,444,445,446,450,451,454,455,457,458,460,463,464

p=479

238個

13,17,19,26,29,31,34,37,38,39,41,43,47,51,52,53,57,58,59,62,65,67,68,74,76,78,79,82,83,85,86,87,91,93,94,95,101,102,104,106,111,113,114,116,117,118,119,123,124,127,129,130,133,134,136,141,143,145,148,149,152,153,155,156,157,158,159,164,166,170,171,172,174,177,179,182,185,186,187,188,190,191,195,199,201,202,203,204,205,208,209,212,215,217,222,223,226,227,228,229,232,234,235,236,237,238,239,246,248,249,254,255,258,259,260,261,263,265,266,268,269,272,273,279,281,282,283,285,286,287,290,295,296,298,299,301,303,304,306,310,311,312,314,316,317,318,319,325,328,329,332,333,335,337,339,340,341,342,344,347,348,351,353,354,357,358,359,364,367,369,370,371,372,374,376,379,380,381,382,383,387,389,390,391,395,398,399,402,404,406,407,408,409,410,413,415,416,418,419,423,424,425,429,430,431,433,434,435,437,439,443,444,446,447,449,451,452,454,455,456,457,458,459,461,463,464,465,467,468,469,470,471,472,473,474,475,476,477

p=487

162個

3,6,10,11,13,14,17,20,22,23,24,28,45,46,47,48,52,54,57,59,63,68,74,75,80,86,87,88,93,94,104,105,108,109,112,113,114,117,118,123,131,136,147,148,149,150,151,153,155,158,160,165,172,173,174,176,180,183,184,190,192,198,199,201,202,209,210,211,213,217,218,219,223,224,226,227,229,231,234,239,243,246,247,250,252,257,262,265,266,275,283,290,291,293,294,306,310,316,318,319,323,325,326,331,333,341,345,346,347,350,353,355,358,359,360,365,366,367,368,371,372,376,377,380,384,385,387,389,390,396,398,402,404,405,406,409,410,411,414,415,416,417,418,422,425,429,432,434,437,445,449,451,454,455,456,457,466,471,472,478,483,485

p=491

168個

2,6,7,8,10,18,19,21,22,23,24,26,28,29,30,34,40,47,50,54,57,59,62,67,69,72,73,74,76,78,82,84,86,87,88,89,90,92,95,98,102,103,112,116,119,120,122,130,140,141,142,145,149,150,151,157,160,166,167,170,171,173,177,188,189,191,193,194,198,201,207,209,211,212,214,216,217,219,222,228,235,242,246,247,250,252,254,258,264,266,267,271,273,276,281,285,286,287,292,296,299,304,306,307,309,311,317,319,322,323,326,328,330,335,336,337,343,344,348,352,356,357,358,359,360,364,366,367,368,370,374,383,384,385,391,392,397,398,406,408,412,416,420,421,423,426,427,430,431,433,436,439,442,443,446,447,452,453,455,458,460,466,475,476,478,480,486,487

p=499

164個

7,10,11,15,17,19,23,28,35,40,41,42,44,50,53,58,60,61,63,65,66,68,71,75,76,79,85,86,87,89,90,92,94,95,98,99,102,112,113,114,129,135,138,141,146,147,153,157,160,163,164,168,171,173,176,179,182,185,193,200,202,205,206,207,210,212,214,217,218,219,223,229,232,238,240,241,242,244,246,252,260,262,264,266,271,272,273,274,275,278,284,286,295,300,301,302,303,304,309,310,311,315,316,318,319,321,325,327,329,340,341,344,347,348,349,356,357,362,363,366,367,368,369,373,376,377,378,379,380,383,390,392,393,394,396,398,399,408,411,415,417,419,426,429,430,442,443,448,450,452,453,454,456,461,465,466,469,470,474,477,478,479,485,494