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节选我以前计算的<素数各个估值公式的比较>录于此,供参考比较
限于篇幅,只给出3个公式13点,(原来选取11个比较有代表性公式,仅取3项)
说明:
N/log(N) --- 素数定理
Lix(m=10)--- 带余项的素数定理 对数积分的 m=10 渐进公式
Rx --- 黎曼和公式
n= 1000 pi= 168
2 N/log(N) = 144.76 r=0.86169540 a= -24
9 Lix(m=10) = 181.58 r=1.08082786 a= 13
11 Rx = 168.22 r=1.00128360 a= 0
n= 10000 pi= 1229
2 N/log(N) = 1085.74 r=0.88343060 a= -144
9 Lix(m=10) = 1247.07 r=1.01469982 a= 18
11 Rx = 1226.72 r=0.99814821 a= -3
n= 100000 pi= 9592
2 N/log(N) = 8685.89 r=0.90553478 a= -907
9 Lix(m=10) = 9628.91 r=1.00384770 a= 36
11 Rx = 9587.15 r=0.99949387 a= -5
n= 1000000 pi= 78498
2 N/log(N) = 72382.41 r=0.92209246 a= -6116
9 Lix(m=10) = 78624.64 r=1.00161333 a= 126
11 Rx = 78527.01 r=1.00036955 a= 29
n= 10000000 pi= 664579
2 N/log(N) = 620420.69 r=0.93355446 a= -44159
9 Lix(m=10) = 664912.29 r=1.00050150 a= 333
11 Rx = 664666.92 r=1.00013229 a= 87
n= 100000000 pi= 5761455
2 N/log(N) = 5428681.02 r=0.94224133 a= -332774
9 Lix(m=10) = 5762196.52 r=1.00012870 a= 741
11 Rx = 5761551.15 r=1.00001669 a= 96
n= 1000000000 pi= 50847534
2 N/log(N) = 48254942.43 r=0.94901244 a= -2592592
9 Lix(m=10) = 50849204.92 r=1.00003286 a= 1670
11 Rx = 50847454.46 r=0.99999844 a= -80
n= 10000000000 pi= 455052511 100亿
2 N/log(N) = 434294481.90 r=0.95438322 a= -20758030
9 Lix(m=10) = 455055533.46 r=1.00000664 a= 3022
11 Rx = 455050681.98 r=0.99999598 a= -1830
n= 100000000000 pi= 4118054813
2 N/log(N) = 3948131653.67 r=0.95873703 a= -169923160
9 Lix(m=10) = 4118066147.88 r=1.00000275 a= 11334
11 Rx = 4118052492.81 r=0.99999944 a= -2321
n=1000000000000 pi= 37607912018
2 N/log(N) = 36191206825.27 r=0.96232960 a= -1416705193
9 Lix(m=10) = 37607949391.55 r=1.00000099 a= 37373
11 Rx = 37607910539.72 r=0.99999996 a= -1479
n=10000000000000 pi= 346065536839
2 N/log(N) =334072678387.12 r=0.96534512 a=-11992858452
9 Lix(m=10) =346065642356.53 r=1.00000030 a= 105517
11 Rx =346065531062.36 r=0.99999998 a= -5777
n=100000000000000 pi= 3204941750802
2 N/log(N) =3102103442166.08 r=0.96791258 a=-102838308636
9 Lix(m=10) =3204942051161.15 r=1.00000009 a= 300359
11 Rx =3204941731596.88 r=0.99999999 a= -19206
n=1000000000000000 pi= 29844570422669
2 N/log(N) =28952965460216.79 r=0.97012505 a=-891604962453
9 Lix(m=10) =29844571409955.07 r=1.00000003 a= 987286
11 Rx =29844570495880.18 r=1.00000000 a= 73211
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IP卡
狗仔卡
发表于 2018-7-1 15:33
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