热切求教老师们对r2(N)≥[(π（N))^2/N]大数据之验证

cuikun-186

热切求教老师们对r2(N)≥[(π（N))^2/N]大数据之验证

cuikun-186

r2(N)≥[(π（N))^2/N]之验证：

r2(6)=3，π（6)=3，r2(6)=3≥[(π（6))^2/6]=[9/6]=1，r2(6)=3≥1【正确】

r2(8)=4，π（8)=4，r2(8)=4≥[(π（8))^2/8]=[16/8]=2，r2(8)=4≥2【正确】

r2(10)=3，π（10)=4，r2(10)=3≥[(π（10))^2/10]=[16/10]=1，r2(10)=3≥1【正确】

r2(12)=3，π（12)=5，r2(12)=4≥[(π（12))^2/12]=[25/12]=2，r2(12)=4≥2【正确】

r2(14)=5，π（14)=6，r2(14)=5≥[(π（14))^2/14]=[36/14]=2，r2(14)=5≥2【正确】

r2(16)=4，π（16)=6，r2(16)=4≥[(π（16))^2/16]=[36/16]=2，r2(16)=4≥2【正确】

r2(18)=6，π（18)=7，r2(18)=6≥[(π（18))^2/18]=[49/18]=3，r2(18)=6≥3【正确】

r2(20)=6，π（20)=8，r2(20)=6≥[(π（20))^2/20]=[64/20]=3，r2(18)=6≥3【正确】

r2(22)=5，π（22)=8，r2(22)=6≥[(π（22))^2/22]=[64/22]=2，r2(22)=5≥2【正确】

cuikun-186

本帖最后由 cuikun-186 于 2023-2-9 09:10 编辑


r2(38)=5，π（38)=12，r2(38)=5≥[(π（38))^2/38]=[144/38]=3，r2(38)=5≥3【正确】

r2(98)=8，π（98)=25，r2(98)=8≥[(π（98))^2/98]=[625/98]=6，r2(98)=8≥6【正确】

r2(100)=12，π（100)=25，r2(100)=12≥[(π（100))^2/100]=[625/100]=6，r2(100)=12≥6【正确】



r2(1000)=56，π（1000)=168，r2(1000)=56≥[(π（1000))^2/1000]=[28224/1000]=28，

r2(1000)=56≥28【正确】

cuikun-186

哥猜表法数r2(N)下限值函数是增函数之简证
崔坤
中国青岛即墨，E-mail:cwkzq@126.com


我的公式是：r2(N)≥[(π（N))^2/N]，[ ]是取整符号，1为素数，偶数N≥6

Treenewbee

cuikun-186 发表于 2023-2-9 16:09
哥猜表法数r2(N)下限值函数是增函数之简证
崔坤
中国青岛即墨，E-mail:cwkzq@126.com

你把你的r2(N)的公式列出来，我可以帮你验证一下

cuikun-186

Treenewbee 发表于 2023-2-9 16:24
你把你的r2(N)的公式列出来，我可以帮你验证一下

老师好！

谢谢您！

您辛苦了！

我的公式是：r2(N)≥[(π（N))^2/N]，[ ]是取整符号，1为素数，偶数N≥6

请老师阅览：

cuikun-186

【1】r2(N)≥[(π（N))^2/N]之验证:

r2(9699722)=56543

π(9699722)= 646031

因为[(π（9699722))^2/9699722]=[ 646031^2/9699722]=43027

r2(9699722)=56543≥43027

故：r2(N)≥[(π（N))^2/N]正确

【2】r2(N)≥[(π（N))^2/N]之验证:

r2(9699724)=61468

π(9699724)= 646031

因为[(π（9699724))^2/9699724]=[ 646031^2/9699724]=43027

r2(9699724)=61468≥43027

故：r2(N)≥[(π（N))^2/N]正确

【3】r2(N)≥[(π（N))^2/N]之验证:

r2(9699726)=113556

π(9699726)= 646031

因为[(π（9699726))^2/9699726]=[ 646031^2/9699726]=43027

r2(9699726)=113556≥43027

故：r2(N)≥[(π（N))^2/N]正确

Treenewbee

cuikun-186 发表于 2023-2-9 16:43
老师好！

谢谢您！

没看明白你的r2(N)咋算的。你把你手头算好的列个表，我帮你验证下

Treenewbee

1000之内的{N，G(N), [(π（N))^2/N]},其中G(N)<[(π（N))^2/N]的序列：

{8,1,2},{12,1,2},{20,2,3},{32,2,3},{38,2,3},{44,3,4},{52,3,4},{56,3,4},{62,3,5},{68,2,5},{80,4,6},{86,5,6},{88,4,6},{92,4,6},{94,5,6},{98,3,6},{104,5,7},{110,6,7},{116,6,7},{118,6,7},{122,4,7},{124,5,7},{128,3,7},{134,6,7},{136,5,7},{140,7,8},{146,6,7},{148,5,7},{152,4,8},{158,5,8},{164,5,8},{166,6,8},{172,6,8},{176,7,9},{178,7,8},{182,6,9},{184,8,9},{188,5,9},{190,8,9},{194,7,9},{200,8,10},{202,9,10},{206,7,10},{208,7,10},{212,6,10},{214,8,10},{218,7,10},{220,9,10},{224,7,10},{226,7,10},{230,9,10},{232,7,10},{236,9,11},{238,9,10},{242,8,11},{244,9,11},{248,6,11},{250,9,11},{254,9,11},{256,8,11},{260,10,11},{262,9,11},{266,8,11},{268,9,11},{272,7,12},{274,11,12},{278,7,12},{284,8,13},{286,12,13},{290,10,12},{292,8,12},{296,8,12},{298,11,12},{302,9,12},{304,10,12},{308,8,12},{314,9,13},{316,10,13},{320,11,13},{322,11,13},{326,7,13},{328,10,13},{332,6,13},{334,11,13},{338,9,13},{344,10,13},{346,9,13},{350,13,14},{352,10,13},{356,9,14},{358,10,14},{362,8,14},{368,8,14},{374,10,14},{376,11,14},{380,13,14},{382,10,14},{386,12,14},{388,9,14},{392,11,15},{394,11,15},{398,7,15},{400,14,15},{404,11,15},{406,13,15},{410,13,15},{412,11,15},{416,10,15},{418,11,15},{422,11,15},{424,12,15},{428,9,15},{430,14,15},{434,13,16},{436,11,16},{440,14,16},{442,13,16},{446,12,16},{448,13,16},{452,12,16},{454,12,16},{458,9,16},{464,12,17},{466,13,17},{470,15,17},{472,13,17},{476,14,17},{478,11,17},{482,11,17},{484,14,17},{488,9,17},{494,13,17},{496,13,17},{500,13,18},{502,15,17},{506,15,18},{508,14,18},{512,11,18},{514,14,18},{518,11,18},{520,17,18},{524,11,18},{526,15,18},{530,14,18},{532,17,18},{536,13,18},{538,14,18},{542,10,18},{544,13,18},{548,11,18},{554,11,18},{556,11,18},{562,14,18},{566,13,18},{568,13,18},{572,11,19},{574,16,19},{578,12,19},{584,12,19},{586,13,19},{590,16,19},{592,15,19},{596,12,19},{598,15,19},{602,12,20},{604,14,20},{608,13,20},{614,15,20},{616,19,20},{620,18,20},{622,17,20},{626,12,20},{628,16,20},{632,10,20},{634,14,20},{638,15,20},{640,18,20},{644,17,21},{646,16,21},{652,15,21},{656,13,21},{658,19,21},{662,14,22},{664,16,22},{668,11,21},{674,15,22},{676,17,22},{680,21,22},{682,16,22},{686,16,22},{688,16,22},{692,11,22},{694,19,22},{698,14,22},{704,18,22},{706,19,22},{710,16,22},{712,17,22},{716,14,22},{718,15,22},{722,14,22},{724,15,22},{728,15,22},{730,21,22},{734,15,23},{736,19,22},{740,18,23},{742,19,23},{746,18,23},{748,19,23},{752,14,23},{754,17,23},{758,15,23},{760,21,23},{764,17,23},{766,17,23},{772,18,23},{776,16,24},{778,15,24},{782,14,24},{784,18,23},{788,15,24},{790,22,24},{794,17,23},{796,14,23},{800,21,24},{802,16,24},{806,16,23},{808,14,23},{812,18,24},{814,20,24},{818,17,24},{820,20,24},{824,16,24},{826,21,24},{830,22,25},{832,22,25},{836,18,25},{838,17,25},{842,18,25},{844,17,25},{848,15,25},{854,20,25},{856,19,25},{860,18,25},{862,17,25},{866,17,25},{868,21,25},{872,18,25},{874,19,25},{878,14,25},{884,21,26},{886,18,26},{890,23,26},{892,19,26},{896,20,26},{898,19,26},{902,15,26},{904,17,26},{908,15,26},{914,20,26},{916,18,26},{920,23,26},{922,20,26},{926,18,26},{928,18,26},{932,17,26},{934,20,26},{938,18,26},{940,24,26},{944,18,27},{946,20,27},{950,25,27},{952,23,27},{956,19,27},{958,22,27},{962,16,27},{964,18,27},{968,17,27},{974,17,27},{976,19,27},{980,26,27},{982,17,27},{986,20,27},{988,23,27},{992,13,28},{994,25,28},{998,17,28}

Treenewbee

100之内的{N，π（N)，G(N), [(π（N))^2/N]},其中G(N)<[(π（N))^2/N]的序列
{8, 4, 1, 2}, {12, 5, 1, 2}, {20, 8, 2, 3}, {32, 11, 2, 3}, {38, 12,
  2, 3}, {44, 14, 3, 4}, {52, 15, 3, 4}, {56, 16, 3, 4}, {62, 18, 3,
  5}, {68, 19, 2, 5}, {80, 22, 4, 6}, {86, 23, 5, 6}, {88, 23, 4,
  6}, {92, 24, 4, 6}, {94, 24, 5, 6}, {98, 25, 3, 6}