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[这个贴子最后由小草在 2008/01/13 00:45pm 第 1 次编辑]
哥德巴赫猜想研究四十二
根据区间套定理
D+(m3)=D(22)=3
D+(m4)=D(210)=19
D+(m5)=D(2310)=114
D+(m6)=D(30030)=905
D+(m7)=D(510510)=9493
D-(m3)=D(12)=1
D-(m4)=D(68)=2
D-(m5)=D(332)=6
D-(m6)=D(2672)=28
D-(m7)=D(33038)=223
(Am3)+=2.729961378
(Am4)+=2.449340349
(Am5)+=2.281956947
(Am6)+=2.206731038
(Am7)+=2.133879510
(Am3)-=1.765543056
(Am4)-=1.433097902
(Am5)-=1.469826109
(Am6)-=1.501008410
(Am7)-=1.546974889
这就是说
6≤x≤30
1≤D(x)≤3
30≤x≤210
2≤D(x)≤19
210≤x≤2310
6≤D(x)≤114
2310≤x≤30030
28≤D(x)≤905
30030≤x≤510510
223≤D(x)≤9493
再精确点取区间m4,A+=2.449340349,A-=1.433097902，则有
32/ln32^A+=[1.524077897]=1≤D(32)≤32/ln32^A-=[5.389769958]=5
34/ln34^A+=[1.551992146]=1≤D(34)≤34/ln34^A-=[5.586067194]=5
36/ln36^A+=[1.579826436]=1≤D(36)≤36/in34^A-=[5.779927979]=5
38/ln38^A+=[1.607537009]=1≤D(38)≤38/ln38^A-=[5.971497420]=5
40/ln40^A+=[1.635093184]=1≤D(40)≤40/ln40^A-=[6.160908021]=6
42/ln42^A+=[1.662473674]=1≤D(42)≤42/ln42^A-=[6.348280780]=6
44/ln44^A+=[1.689664004]=1≤D(44)≤44/ln44^A-=[6.533726303]=6
46/ln46^A+=[1.716654694]=1≤D(46)≤46/ln46^A-=[6.717345843]=6
48/ln48^A+=[1.743439937]=1≤D(48)≤48/ln48^A-=[6.899232263]=6
50/ln50^A+=[1.770016653]=1≤D(50)≤50/ln50^A-=[7.079470897]=7
52/ln52^A+=[1.796383778]=1≤D(52)≤52/ln52^A-=[7.258140325]=7
54/ln54^A+=[1.822541750]=1≤D(54)≤54/ln54^A-=[7.435313063]=7
56/ln56^A+=[1.848492115]=1≤D(56)≤56/ln56^A-=[7.611056165]=7
58/ln58^A+=[1.874237237]=1≤D(58)≤58/ln58^A-=[7.785431770]=7
60/ln60^A+=[1.899780070]=1≤D(60)≤60/ln60^A-=[7.958497570]=7
62/ln62^A+=[1.925123996]=1≤D(62)≤62/ln62^A-=[8.130307240]=8
64/ln64^A+=[1.950272691]=1≤D(64)≤64/ln64^A-=[8.300910808]=8
66/ln66^A+=[1.975230028]=1≤D(66)≤66/ln66^A-=[8.470354987]=8
68/ln68^A+=[2] =2≤D(68)≤68/ln68^A-=[8.638683473]=8
70/ln70^A+=[2.024586666]=2≤D(70)≤70/ln70^A-=[8.805937208]=8
72/ln72^A+=[2.048994100]=2≤D(72)≤72/ln72^A-=[8.972154615]=8
74/ln74^A+=[2.073226365]=2≤D(74)≤74/ln74^A-=[9.137371809]=9
76/ln76^A+=[2.097287480]=2≤D(76)≤76/ln76^A-=[9.301622784]=9
78/ln78^A+=[2.121181409]=2≤D(78)≤78/ln78^A-=[9.464939588]=9
80/ln80^A+=[2.144912039]=2≤D(80)≤80/ln80^A-=[9.627352470]=9
82/ln82^A+=[2.168483175]=2≤D(82)≤82/ln82^A-=[9.788890021]=9
84/ln84^A+=[2.191898530]=2≤D(84)≤84/ln84^A-=[9.949579300]=9
86/ln86^A+=[2.215161723]=2≤D(86)≤86/ln86^A-=[10.10944594]=10
88/ln88^A+=[2.238276274]=2≤D(88)≤88/ln88^A-=[10.26851428]=10
90/ln90^A+=[2.261245602]=2≤D(90)≤90/ln90^A-=[10.42680739]=10
92/in92^A+=[2.284073026]=2≤D(92)≤92/ln92^A-=[10.58434724]=10
94/ln94^A+=[2.306761767]=2≤D(94)≤94/ln94^A-=[10.74115474]=10
96/ln96^A+=[2.329314946]=2≤D(96)≤96/ln96^A-=[10.89724977]=10
98/ln98^A+=[2.351735586]=2≤D(98)≤98/ln98^A-=[11.05265132]=11
100/ln100^A+=[2.374026618]=2≤D(100)≤100/ln100^A-=[11.20737752]=11
102/ln102^A+=[2.396190877]=2≤D(102)≤
102/ln102^A-=[11.36144565]=11
104/ln104^A+=[2.418231112]=2≤D(104)≤
104/ln104^A-=[11.51487227]=11
106/ln106^A+=[2.440149982]=2≤D(106)≤
106/ln106^A-=[11.66767320]=11
108/ln108^A+=[2.461950061]=2≤D(108)≤
108/ln108^A-=[11.81986361]=11
110/ln110^A+=[2.483633844]=2≤D(110)≤
110/ln110^A-=[11.97145802]=11
112/ln112^A+=[2.505203744]=2≤D(112)≤
112/ln112^A-=[12.12247036]=12
114/ln114^A+=[2.526662100]=2≤D(114)≤
114/ln114^A-=[12.27291401]=12
116/ln116^A+=[2.548011175]=2≤D(116)≤
116/ln116^A-=[12.42280180]=12
118/ln118^A+=[2.569253164]=2≤D(118)≤
118/ln118^A-=[12.57214609]=12
120/ln120^A+=[2.590390192]=2≤D(120)≤
120/ln120^A-=[12.72095873]=12
122/ln122^A+=[2.611424318]=2≤D(122)≤
122/ln122^A-=[12.86925116]=12
124/ln124^A+=[2.632357538]=2≤D(124)≤
124/ln124^A-=[13.01703436]=13
126/ln126^A+=[2.653191788]=2≤D(126)≤
126/ln126^A-=[13.16431895]=13
128/ln128^A+=[2.673928943]=2≤D(128)≤
128/ln128^A-=[13.31111512]=13
130/ln130^A+=[2.694570825]=2≤D(130)≤
130/ln130^A-=[13.45743273]=13
132/ln132^A+=[2.715119198]=2≤D(132)≤
132/ln132^A-=[13.60328130]=13
134/ln134^A+=[2.735575777]=2≤D(134)≤
134/ln134^A-=[13.74867000]=13
136/ln136^A+=[2.755942224]=2≤D(136)≤
136/ln136^A-=[13.89360771]=13
138/ln138^A+=[2.776220154]=2≤D(138)≤
138/ln138^A-=[14.03810299]=14
140/ln140^A+=[2.796411135]=2≤D(140)≤
140/ln140^A-=[14.18216414]=14
142/ln142^A+=[2.816516692]=2≤D(142)≤
142/ln142^A-=[14.32579918]=14
144/ln144^A+=[2.836538303]=2≤D(144)≤
144/ln144^A-=[14.46901587]=14
146/ln146^A+=[2.856477407]=2≤D(146)≤
146/ln146^A-=[14.61182173]=14
148/ln148^A+=[2.876335403]=2≤D(148)≤
148/ln148^A-=[14.75422405]=14
150/ln150^A+=[2.896113651]=2≤D(150)≤
150/ln150^A-=[14.89622987]=14
152/ln152^A+=[2.915813474]=2≤D(152)≤
152/ln152^A-=[15.03784605]=15
154/ln154^A+=[2.935436157]=2≤D(154)≤
154/ln154^A-=[15.17907923]=15
156/ln156^A+=[2.954982954]=2≤D(156)≤
156/ln156^A-=[15.31993584]=15
158/ln158^A+=[2.974455083]=2≤D(158)≤
158/ln158^A-=[15.46042214]=15
160/ln160^A+=[2.993853732]=2≤D(160)≤
160/ln160^A-=[15.60054420]=15
162/ln162^A+=[3.013180055]=3≤D(162)≤
162/ln162^A-=[15.74030792]=15
164/ln164^A+=[3.032435179]=3≤D(164)≤
164/ln164^A-=[15.87971904]=15
166/ln166^A+=[3.051620201]=3≤D(166)≤
166/ln166^A-=[16.01878311]=16
168/ln168^A+=[3.070736190]=3≤D(168)≤
168/ln168^A-=[16.15750557]=16
170/ln170^A+=[3.089784187]=3≤D(170)≤
170/ln170^A-=[16.29589168]=16
172/ln172^A+=[3.108765210]=3≤D(172)≤
172/ln172^A-=[16.43394658]=16
174/ln174^A+=[3.127680248]=3≤D(174)≤
174/ln174^A-=[16.57167525]=16
176/ln176^A+=[3.146530269]=3≤D(176)≤
176/ln176^A-=[16.70908256]=16
178/ln178^A+=[3.165316216]=3≤D(178)≤
178/ln178^A-=[16.84617323]=16
180/ln180^A+=[3.184039009]=3≤D(180)≤
180/ln180^A+=[16.98295189]=16
182/ln182^A+=[3.202699547]=3≤D(182)≤
182/ln182^A-=[17.11942303]=17
184/ln184^A+=[3.221298707]=3≤D(184)≤
184/ln184^A-=[17.25559104]=17
186/ln186^A+=[3.239837345]=3≤D(186)≤
186/ln186^A-=[17.39146017]=17
188/ln188^A+=[3.258316299]=3≤D(188)≤
188/ln188^A-=[17.52703461]=17
190/ln190^A+=[3.276736385]=3≤D(190)≤
190/ln190^A-=[17.66231841]=17
192/ln192^A+=[3.295098402]=3≤D(192)≤
192/ln192^A-=[17.79731555]=17
194/ln194^A+=[3.313403131]=3≤D(194)≤
194/ln194^A-=[17.93202990]=17
196/ln196^A+=[3.331651336]=3≤D(196)≤
196/ln196^A-=[18.06646523]=18
198/ln198^A+=[3.349843761]=3≤D(198)≤
198/ln198^A-=[18.20062525]=18
200/ln200^A+=[3.367981137]=3≤D(200)≤
200/ln200^A-=[18.33451355]=18
202/ln202^A+=[3.386064178]=3≤D(202)≤
202/ln202^A-=[18.46813367]=18
204/ln204^A+=[3.404093581]=3≤D(204)≤
204/ln204^A-=[18.60148905]=18
206/ln206^A+=[3.422070030]=3≤D(206)≤
206/ln206^A-=[18.73458305]=18
208/ln208^A+=[3.439994193]=3≤D(208)≤
208/ln208^A-=[18.86741896]=18
210/ln210^A+=[3.457866724]=3≤D(210)≤
210/ln210^A-=[19] =19
再精确一点，取区间m4,A+=2.449340349,我们有
D(32)≈32/ln32^A+=[1.524077897]=1
D(34)≈34/ln34^A+(16/15)=[1.655458289]=1
D(36)≈36/ln36^A+(2/1)=[3.159652872]=3
D(38)≈38/ln38^A+(18/17)=[1.702098010]=1
D(40)≈40/ln40^A+(4/3)=[2.180124245]=2
D(42)≈42/ln42^A+(2/1)(6/5)=[3.989936818]=3
D(44)≈44/ln44^A+(10/9)=[1.877404449]=1
D(46)≈46/ln46^A+(22/21)=[1.798400156]=1
D(48)≈48/ln48^A+(2/1)=[3.486879874]=3
D(50)≈50/ln50^A+(4/3)=[2.360022204]=2
D(52)≈52/ln52^A+(12/11)=[1.959691394]=1
D(54)≈54/ln54^A+(2/1)=[3.645083500]=3
D(56)≈56/ln56^A+(6/5)=[2.218178538]=2
D(58)≈58/ln58^A+(28/27)=[1.943653431]=1
D(60)≈60/ln60^A+(2/1)(4/3)=[5.066080187]=5
D(62)≈62/ln62^A+(30/29)=[1.991507582]=1
D(64)≈64/ln64^A+=[2.017523473]=2
D(66)≈66/ln66^A+(2/1)(10/9)=[4.389400062]=4
D(68)≈68/ln68^A+(16/15)=[2.133333333]=2
D(70)≈70/ln70^A+(4/3)(6/5)=[3.239338666]=3
D(72)≈72/ln72^A+(2/1)=[4.097988200]=4
D(74)≈74/ln74^A+(36/35)=[2.132461404]=2
D(76)≈76/ln76^A+(18/17)=[2.220657332]=2
D(78)≈78/ln78^A+(2/1)(12/11)=[4.628032165]=4
D(80)≈80/ln80^A+(4/3)=[2.859882719]=2
D(82)≈82/ln82^A+(40/39)=[2.224085308]=2
D(84)≈84/ln84^A+(2/1)(6/5)=[5.260556472]=5
D(86)≈86/ln86^A+(42/41)=[2.269190058]=2
D(88)≈88/ln88^A+(10/9)=[2.486973638]=2
D(90)≈90/ln90^A+(2/1)(4/3)=[6.029988272]=6
D(92)≈92/ln92^A+(22/21)=[2.392838408]=2
D(94)≈94/ln94^A+(46/45)=[2.358023140]=2
D(96)≈96/ln96^A+(2/1)=[4.658629892]=4
D(98)≈98/ln98^A+(6/5)=[2.822082703]=2
D(100)≈100/ln100^A+(4/3)=[3.165368824]=3
D(102)≈102/ln102^A+(2/1)(16/15)=[5.111873871]=5
D(104)≈104/ln104^A+(12/11)=[2.638070304]=2
D(106)≈106/ln106^A+(52/51)=[2.487996060]=2
D(108)≈108/ln108^A+(2/1)=[4.923900122]=4
D(110)≈110/1n110^A+(4/3)(10/9)=[3.679457546]=3
D(112)≈112/ln112^A+(6/5)=[3.006244493]=3
D(114)≈114/ln114^A+(2/1)(18/17)=[5.350578565]=5
D(116)≈116/ln116^A+(28/27)=[2.642381959]=2
D(118)≈118/ln118^A+(58/57)=[2.614327781]=2
D(120)≈120/ln120^A+(2/1)(4/3)=[6.907707179]=6
D(122)≈122/ln122^A+(60/59)=[2.655685747]=2
D(124)≈124/ln124^A+(30/29)=[2.723128488]=2
D(126)≈126/ln126^A+(2/1)(6/5)=[6.367660291]=6
D(128)≈128/ln128^A+=[2.673928943]=2
D(130)≈130/ln130^A+(4/3)(12/11)=[3.919375744]=3
D(132)≈132/ln132^A+(2/1)(10/9)=[6.033598218]=6
D(134)≈134/ln134^A+(66/65)=[2.777661558]=2
D(136)≈136/ln136^A+(16/15)=[2.939671706]=2
D(138)≈138/ln138^A+(2/1)(22/21)=[5.816842227]=5
D(140)≈140/ln140^A+(4/3)(6/5)=[4.474257815]=4
D(142)≈142/ln142^A+(70/69)=[2.857335774]=2
D(144)≈144/ln144^A+(2/1)=[5.673076606]=5
D(146)≈146/ln146^A+(72/71)=[2.896709483]=2
D(148)≈148/ln148^A+(36/35)=[2.958516415]=2
D(150)≈150/ln150^A+(2/1)(4/3)=[7.722969736]=7
D(152)≈152/ln152^A+(18/17)=[3.087331914]=3
D(154)≈154/ln154^A+(6/5)(10/9)=[3.913914876]=3
D(156)≈156/ln156^A+(2/1)(12/11)=[6.447235536]=6
D(158)≈158/ln158^A+(78/77)=[3.013084370]=3
D(160)≈160/ln160^A+(4/3)=[3.991804976]=3
D(162)≈162/ln162^A+(2/1)=[6.026360110]=6
D(164)≈164/ln164^A+(40/39)=[3.110189927]=3
D(166)≈166/ln166^A+(82/81)=[3.089294524]=3
D(168)≈168/ln168^A+(2/1)(6/5)=[7.369766856]=7
D(170)≈170/ln170^A+(4/3)(16/15)=[4.394359732]=4
D(172)≈172/ln172^A+(42/41)=[3.184588752]=3
D(174)≈174/ln174^A+(2/1)(28/27)=[6.487040514]=6
D(176)≈176/ln176^A+(10/9)=[3.496144743]=3
D(178)≈178/ln178^A+(88/87)=[3.201699464]=3
D(180)≈180/ln180^A+(2/1)(4/3)=[8.490770691]=8
D(182)≈182/ln182^A+(6/5)(12/11)=[4.192624862]=4
D(184)≈184/ln184^A+(22/21)=[3.374693884]=3
D(186)≈186/ln186^A+(2/1)(30/29)=[3.351555874]=3
D(188)≈188/ln188^A+(46/45)=[3.330723328]=3
D(190)≈190/ln190^A+(4/3)(18/17)=[4.625980778]=4
D(192)≈192/ln192^A+(2/1)=[6.590196804]=6
D(194)≈194/ln194^A+(96/95)=[3.348281059]=3
D(196)≈196/ln196^A+(6/5)=[3.997981603]=3
D(198)≈198/ln198^A+(2/1)(10/9)=[3.722048623]=3
D(200)≈200/ln200^A+(4/3)=[4.490641516]=4
D(202)≈202/ln202^A+(100/99)=[3.454814996]=3
D(204)≈204/ln204^A+(2/1)(16/15)=[7.262066306]=7
D(206)≈206/ln206^A+(102/101)=[3.455951911]=3
D(208)≈208/ln208^A+(12/11)=[3.752720938]=3
D(210)≈210/ln210^A+(2/1)(4/3)(6/5)=[11.06517351]=11
取一个任意偶数30030,就有
D(30030)≈30030/ln30030^2.729961378(2/1)(4/3)(6/5)(10/9)(12/11)=[199.5720869]=199
再精确一点
D(30030)≈30030/ln30030^2.449340349(2/1)(4/3)(6/5)(10/9)(12/11)=[384.0970437]=384
再精确一点
D(30030)≈30030/ln30030^2.281956947(2/1)(4/3)(6/5)(10/9)(12/11)=[567.6012062]=567
再精确一点
D(30030)≈30030/ln30030^2.206731038(2/1)(4/3)(6/5)(10/9)(12/11)=[676.4979147]=676
愈接近区间mk的A+值，计算就愈正确。
作者施承忠 2008-1-13
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