G(N)≈1.40625KN/(lnN)^2 (双记法)
①当偶数N不能被6整除,则K=2/3
②当偶数N能被6整除,而不能被5整除。则K=1
③当偶数N分别能被6和5整除,则K=4/3
以下为大偶数素数对真值与公式计算值比较,(素数对真值引自S云淡风清X先生提供的资料)
(素数对真值-函数公式计算值)/素数对真值=相对误差
------------N---------素数对真值-------公式计算值-------相对误差
D(2024072300) = 4286313----------4132556------------0.036
D(2024072302) = 3857928----------4132556------------负0.071
D(2024072304) = 6428816----------6198834------------0.036
D(2024072306) = 3214940----------4132556------------负0.285
D(2024072308) = 3216880----------4132556------------负0.285
D(2024072310) = 9347828----------8265112------------0.116
D(2024072312) = 3366107----------4132556-----------负0.228
D(2024072314) = 3621412----------4132556------------负0.141
D(2024072316) = 7731433----------6198834------------0.198
D(2024072318) = 3404831----------4132556------------负0.214
D(2024072320) = 4378824----------4132556------------0.056
D(2024072322) = 6488219----------6198834------------0.045
D(2024072324) = 3214016----------4132556------------负0.286
D(2024072326) = 3429693----------4132556------------负0.205
D(2024072328) = 6428127-----------6198834------------0.036
D(2024072330) = 5144183----------4132556------------0.197
D(2024072332) = 3276996----------4132556------------负0261
D(2024072334) = 6440739----------6198834------------0.038
D(2024072336) = 4030721----------4132556------------负0.025
D(2024072338) = 3301242----------4132556------------负0.252
D(2024072340) = 8573535----------8265112------------0.047
D(2024072342) = 3332546----------4132556------------负0.240
D(2024072344) = 3861141----------4132556------------负0.070
D(2024072346) = 6607706----------6198834------------0.062
D(2024072348) = 3254069----------4132556------------负0.270
D(2024072350) = 4389017----------4132556------------0.058
D(2024072352) = 6427501----------6198834------------0.036
D(2024072354) = 3333979----------4132556------------负0.240
D(2024072356) = 3409959----------4132556------------负0.212
D(2024072358) = 9028084----------6198834------------0.313
D(2024072360) = 4592000----------4132556------------0.100
D(2024072362) = 3560215----------4132556------------负0.161
D(2024072364) = 6490731----------6198834------------0.045
D(2024072366) = 3213566----------4132556------------负0.286
D(2024072368) = 3211931----------4132556------------负0.287
D(2024072370) = 8583762----------8265112------------0.037
D(2024072372) = 3860217----------4132556------------负0.071
D(2024072374) = 3213721----------4132556------------负0.286
D(2024072376) = 6485784----------6198834------------0.044
D(2024072378) = 3214862----------4132556-----------负0.285
D(2024072380) = 4759867----------4132556------------0.132
D(2024072382) = 6467825----------6198834------------0.042
D(2024072384) = 3214188----------4132556------------负0.286
D(2024072386) = 3879035----------4132556------------负0.065
D(2024072388) = 7012382----------6198834------------0.112
D(2024072390) = 4379202----------4132556------------0.056
D(2024072392) = 3212716----------4132556------------负0.286
D(2024072394) = 7270399----------6198834------------0.147
D(2024072396) = 3212341----------4132556------------负0.286
D(2024072398) = 3363413----------4132556------------负0.229