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“全国高校素质教育教材研究编审委员会”冲破了权威对猜想证明的垄断
用概率方法计算素数的数量,相对误差也不大。
概率计算的数量用Sp(x)表示,相对误差用E表示;
素数定理的计算数量x / ln x用Gs表示,其相对误差用E2 表示。
计算示例:
in [2, 1000 ]: π(X)= 168 Sp(x)= 159.11 E=-.053 Gs(x)= 144.76 E2=-.138
in [2, 2000 ]: π(X)= 303 Sp(x)= 291.34 E=-.038 Gs(x)= 263.13 E2=-.132
in [2, 3000 ]: π(X)= 430 Sp(x)= 417.05 E=-.03 Gs(x)= 374.7 E2=-.129
in [2, 4000 ]: π(X)= 550 Sp(x)= 536.32 E=-.025 Gs(x)= 482.27 E2=-.123
in [2, 5000 ]: π(X)= 669 Sp(x)= 658.43 E=-.016 Gs(x)= 587.05 E2=-.122
in [2, 6000 ]: π(X)= 783 Sp(x)= 768.08 E=-.019 Gs(x)= 689.69 E2=-.119
in [2, 7000 ]: π(X)= 900 Sp(x)= 873.46 E=-.029 Gs(x)= 790.63 E2=-.122
in [2, 8000 ]: π(X)= 1007 Sp(x)= 985.74 E=-.021 Gs(x)= 890.16 E2=-.116
in [2, 9000 ]: π(X)= 1117 Sp(x)= 1107.32 E=-.009 Gs(x)= 988.47 E2=-.115
in [2, 10000 ]: π(X)= 1229 Sp(x)= 1216.5 E=-.01 Gs(x)= 1085.74 E2=-.117
in [2, 20000 ]: π(X)= 2262 Sp(x)= 2245.83 E=-.007 Gs(x)= 2019.49 E2=-.107
in [2, 30000 ]: π(X)= 3245 Sp(x)= 3238.72 E=-.002 Gs(x)= 2910.09 E2=-.103
in [2, 40000 ]: π(X)= 4203 Sp(x)= 4181.11 E=-.005 Gs(x)= 3774.78 E2=-.102
in [2, 50000 ]: π(X)= 5133 Sp(x)= 5171.97 E= .008 Gs(x)= 4621.17 E2=-.1
in [2, 60000 ]: π(X)= 6057 Sp(x)= 6074 E= .003 Gs(x)= 5453.5 E2=-.1
in [2, 70000 ]: π(X)= 6935 Sp(x)= 7000.6 E= .009 Gs(x)= 6274.51 E2=-.095
in [2, 80000 ]: π(X)= 7837 Sp(x)= 7883.55 E= .006 Gs(x)= 7086.05 E2=-.096
in [2, 90000 ]: π(X)= 8713 Sp(x)= 8804.71 E= .011 Gs(x)= 7889.5 E2=-.095
in [2, 100000 ]: π(X)= 9592 Sp(x)= 9686.73 E= .01 Gs(x)= 8685.89 E2=-.094
in [2, 200000 ]: π(X)= 17984 Sp(x)= 18312.86 E= .018 Gs(x)= 16385.29 E2=-.089
in [2, 300000 ]: π(X)= 25997 Sp(x)= 26628.83 E= .024 Gs(x)= 23787.74 E2=-.085
in [2, 400000 ]: π(X)= 33860 Sp(x)= 34667.03 E= .024 Gs(x)= 31009.63 E2=-.084
in [2, 500000 ]: π(X)= 41538 Sp(x)= 42615.18 E= .026 Gs(x)= 38102.89 E2=-.083
in [2, 600000 ]: π(X)= 49098 Sp(x)= 50380.15 E= .026 Gs(x)= 45096.9 E2=-.081
in [2, 700000 ]: π(X)= 56543 Sp(x)= 58193.57 E= .029 Gs(x)= 52010.44 E2=-.08
in [2, 800000 ]: π(X)= 63951 Sp(x)= 65814.13 E= .029 Gs(x)= 58856.56 E2=-.08
in [2, 900000 ]: π(X)= 71274 Sp(x)= 73476.84 E= .031 Gs(x)= 65644.8 E2=-.079
in [2, 1000000 ]: π(X)= 78498 Sp(x)= 81052.53 E= .033 Gs(x)= 72382.41 E2=-.078
in [2, 2000000 ]: π(X)= 148933 Sp(x)= 154670.5 E= .039 Gs(x)= 137848.7 E2=-.074
in [2, 3000000 ]: π(X)= 216816 Sp(x)= 225223 E= .039 Gs(x)= 201151.6 E2=-.072
in [2, 4000000 ]: π(X)= 283146 Sp(x)= 294842 E= .041 Gs(x)= 263126.7 E2=-.071
in [2, 5000000 ]: π(X)= 348513 Sp(x)= 363658.8 E= .043 Gs(x)= 324150.2 E2=-.07
in [2, 6000000 ]: π(X)= 412849 Sp(x)= 430445.9 E= .043 Gs(x)= 384436.2 E2=-.069
in [2, 7000000 ]: π(X)= 476648 Sp(x)= 498431.1 E= .046 Gs(x)= 444122.4 E2=-.068
in [2, 8000000 ]: π(X)= 539777 Sp(x)= 563802.4 E= .045 Gs(x)= 503304.4 E2=-.068
in [2, 9000000 ]: π(X)= 602489 Sp(x)= 629911.8 E= .046 Gs(x)= 562052.6 E2=-.067
in [2, 10000000]: π(X)= 664579 Sp(x)= 696241.3 E= .048 Gs(x)= 620420.7 E2=-.066
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