π, x / ln x, li x の表

ウィキペディア小見出し辞書

π(x), x / ln x, li x の表

出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2022/05/30 10:00 UTC 版)

「素数定理」の記事における「π(x), x / ln x, li x の表」の解説

表は π(x) 、 x / ln x 、 li x の値とそれらの比較の表である。 近似の様子xπ(x)π(x) − x / ln xπ(x) / (x / ln x)li x − π(x)x / π(x)x / ln xli x10 4 −0.343 0.921 2.166 2.500 4.343 6.166 102 25 3.285 1.151 5.126 4.000 21.715 30.126 103 168 23 1.161 10 5.952 145 178 104 1,229 143 1.132 17 8.137 1,086 1,246 105 9,592 906 1.104 38 10.425 8,686 9,630 106 78,498 6,116 1.084 130 12.740 72,382 78,628 107 664,579 44,158 1.071 339 15.047 620,421 664,918 108 5,761,455 332,774 1.061 754 17.357 5,428,681 5,762,209 109 50,847,534 2,592,592 1.054 1,701 19.667 48,254,942 50,849,235 1010 455,052,511 20,758,029 1.048 3,104 21.975 434,294,482 455,055,615 1011 4,118,054,813 169,923,159 1.043 11,588 24.283 3,948,131,654 4,118,066,401 1012 37,607,912,018 1,416,705,193 1.039 38,263 26.590 36,191,206,825 37,607,950,281 1013 346,065,536,839 11,992,858,452 1.034 108,971 28.896 334,072,678,387 346,065,645,810 1014 3,204,941,750,802 102,838,308,636 1.033 314,890 31.202 3,102,103,442,166 3,204,942,065,692 1015 29,844,570,422,669 891,604,962,452 1.031 1,052,619 33.507 28,952,965,460,217 29,844,571,475,288 1016 279,238,341,033,925 7,804,289,844,393 1.029 3,214,632 35.812 271,434,051,189,532 279,238,344,248,557 1017 2,623,557,157,654,233 68,883,734,693,281 1.027 7,956,589 38.116 2,554,673,422,960,305 2,623,557,165,610,822 1018 24,739,954,287,740,860 612,483,070,893,536 1.025 21,949,555 40.420 24,127,471,216,847,324 24,739,954,309,690,415 1019 234,057,667,276,344,607 5,481,624,169,369,960 1.024 99,877,775 42.725 228,576,043,106,974,646 234,057,667,376,222,382 1020 2,220,819,602,560,918,840 49,347,193,044,659,701 1.023 222,744,644 45.028 2,171,472,409,516,259,138 2,220,819,602,783,663,484 1021 21,127,269,486,018,731,928 446,579,871,578,168,707 1.022 597,394,254 47.332 20,680,689,614,440,563,221 21,127,269,486,616,126,182 1022 201,467,286,689,315,906,290 4,060,704,006,019,620,994 1.021 1,932,355,208 49.636 197,406,582,683,296,285,296 201,467,286,691,248,261,498 1023 1,925,320,391,606,803,968,923 37,083,513,766,578,631,309 1.020 7,250,186,216 51.939 1,888,236,877,840,225,337,614 1,925,320,391,614,054,155,139 1024 18,435,599,767,349,200,867,866 339,996,354,713,708,049,069 1.019 17,146,907,278 54.243 18,095,603,412,635,492,818,797 18,435,599,767,366,347,775,144 1025 176,846,309,399,143,769,411,680 3,128,516,637,843,038,351,228 1.018 55,160,980,939 56.546 173,717,792,761,300,731,060,452 176,846,309,399,198,930,392,619 1026 1,699,246,750,872,437,141,327,603 28,883,358,936,853,188,823,261 1.017 155,891,678,121 58.850 1,670,363,391,935,583,952,504,342 1,699,246,750,872,593,033,005,724 1027 16,352,460,426,841,680,446,427,399 267,479,615,610,131,274,163,365 1.0166 508,666,658,006 61.153 16,084,980,811,231,549,172,264,034 16,352,460,426,842,189,113,085,405 1028 157,589,269,275,973,410,412,739,598 2,484,097,167,669,186,251,622,127 1.016 1,427,745,660,374 63.456 155,105,172,108,304,224,161,117,471 157,589,269,275,974,838,158,399,972 π(1024) の値はもともとリーマン予想を仮定して計算されたが[リンク切れ]、その後無条件で証明された。