Λ(sk)和它的延拓

小草

表Λ(sk)=1+∑pk^sk.
π(p^2)=Λ(sk)


原始区域
π(1)=0
π(2)=2^0=1

2^2区域
π(3)=1+2^0=2
π(4)=1+2^0=2

3^2区域
π(5)=2+3^0=3
π(6)=2+3^0=3
π(7)=2+3^0.63092975357145743709952711434278=4
π(8)=2+3^0.63092975357145743709952711434278=4
π(9)=2+3^0.63092975357145743709952711434278=4

5^2区域
π(10)=4
π(11)=4+5^0=5
π(12)=4+5^0=5
π(13)=4+5^0.43067655807339305067010656876396=6
π(14)=4+5^0.43067655807339305067010656876396=6
π(15)=4+5^0.43067655807339305067010656876396=6
π(16)=4+5^0.43067655807339305067010656876396=6
π(17)=4+5^0.68260619448598529513456635927103=7
π(18)=4+5^0.68260619448598529513456635927103=7
π(19)=4+5^0.86135311614678610134021313752795=8
π(20)=4+5^0.86135311614678610134021313752795=8
π(21)=4+5^0.86135311614678610134021313752795=8
π(22)=4+5^0.86135311614678610134021313752795=8
π(23)=4+5^1=9
π(24)=4+5^1=9
π(25)=4+5^1=9

7^2区域
π(26)=9
π(27)=9
π(28)=9
π(29)=9+7^0=10
π(30)=9+7^0=10
π(31)=9+7^0.35620718710802217651417707800129=11
π(32)=9+7^0.35620718710802217651417707800129=11
π(33)=9+7^0.35620718710802217651417707800129=11
π(34)=9+7^0.35620718710802217651417707800129=11
π(35)=9+7^0.35620718710802217651417707800129=11
π(36)=9+7^0.35620718710802217651417707800129=11
π(37)=9+7^0.56457503405357961380455016717489=12
π(38)=9+7^0.56457503405357961380455016717489=12
π(39)=9+7^0.56457503405357961380455016717489=12
π(40)=9+7^0.56457503405357961380455016717489=12
π(41)=9+7^0.7124143742160443530283541560026=13
π(42)=9+7^0.7124143742160443530283541560026=13
π(43)=9+7^0.82708747534691615030375148364557=14
π(44)=9+7^0.82708747534691615030375148364557=14
π(45)=9+7^0.82708747534691615030375148364557=14
π(46)=9+7^0.82708747534691615030375148364557=14
π(47)=9+7^0.92078222116160179031872724517619=15
π(48)=9+7^0.92078222116160179031872724517619=15
π(49)=9+7^0.92078222116160179031872724517619=15

小草

11^2区域
π(50)=15
π(51)=15
π(52)=15
π(53)=15+11^0=16
π(54)=15+11^0=16
π(55)=15+11^0=16
π(56)=15+11^0=16
π(57)=15+11^0=16
π(58)=15+11^0=16
π(59)=15+11^0.28906482631788785926621100770027=17
π(60)=15+11^0.28906482631788785926621100770027=17
π(61)=15+11^0.45815690999132622248221823389275=18
π(62)=15+11^0.45815690999132622248221823389275=18
π(63)=15+11^0.45815690999132622248221823389275=18
π(64)=15+11^0.45815690999132622248221823389275=18
π(65)=15+11^0.45815690999132622248221823389275=18
π(66)=15+11^0.45815690999132622248221823389275=18
π(67)=15+11^0.57812965263577571853242201540055=19
π(68)=15+11^0.57812965263577571853242201540055=19
π(69)=15+11^0.57812965263577571853242201540055=19
π(70)=15+11^0.57812965263577571853242201540055=19
π(71)=15+11^0.67118774147123963813990063731901=20
π(72)=15+11^0.67118774147123963813990063731901=20
π(73)=15+11^0.74722173630921408174842924159302=21
π(74)=15+11^0.74722173630921408174842924159302=21
π(75)=15+11^0.74722173630921408174842924159302=21
π(76)=15+11^0.74722173630921408174842924159302=21
π(77)=15+11^0.74722173630921408174842924159302=21
π(78)=15+11^0.74722173630921408174842924159302=21
π(79)=15+11^0.81150756295724893966795059294056=22
π(80)=15+11^0.81150756295724893966795059294056=22
π(81)=15+11^0.81150756295724893966795059294056=22
π(82)=15+11^0.81150756295724893966795059294056=22
π(83)=15+11^0.86719447895366357779863302310079=23
π(84)=15+11^0.86719447895366357779863302310079=23
π(85)=15+11^0.86719447895366357779863302310079=23
π(86)=15+11^0.86719447895366357779863302310079=23
π(87)=15+11^0.86719447895366357779863302310079=23
π(88)=15+11^0.86719447895366357779863302310079=23
π(89)=15+11^0.91631381998265244496443646778554=24
π(90)=15+11^0.91631381998265244496443646778554=24
π(91)=15+11^0.91631381998265244496443646778554=24
π(92)=15+11^0.91631381998265244496443646778554=24
π(93)=15+11^0.91631381998265244496443646778554=24
π(94)=15+11^0.91631381998265244496443646778554=24
π(95)=15+11^0.91631381998265244496443646778554=24
π(96)=15+11^0.91631381998265244496443646778554=24
π(97)=15+11^0.96025256778912749740611164501929=25
π(98)=15+11^0.96025256778912749740611164501929=25
π(99)=15+11^0.96025256778912749740611164501929=25
π(100)=15+11^0.96025256778912749740611164501929=25
π(101)=15+11^1=26
π(102)=15+11^1=26
π(103)=15+11^1.0362865626271019410146402492933=27
π(104)=15+11^1.0362865626271019410146402492933=27
π(105)=15+11^1.0362865626271019410146402492933=27
π(106)=15+11^1.0362865626271019410146402492933=27
π(107)=15+11^1.069666964424268709138601773948=28
π(108)=15+11^1.069666964424268709138601773948=28
π(109)=15+11^1.1005723892751367989341616006408=29
π(110)=15+11^1.1005723892751367989341616006408=29
π(111)=15+11^1.1005723892751367989341616006408=29
π(112)=15+11^1.1005723892751367989341616006408=29
π(113)=15+11^1.1293446514625658606221188712118=30
π(114)=15+11^1.1293446514625658606221188712118=30
π(115)=15+11^1.1293446514625658606221188712118=30
π(116)=15+11^1.1293446514625658606221188712118=30
π(117)=15+11^1.1293446514625658606221188712118=30
π(118)=15+11^1.1293446514625658606221188712118=30
π(119)=15+11^1.1293446514625658606221188712118=30
π(120)=15+11^1.1293446514625658606221188712118=30
π(121)=15+11^1.1293446514625658606221188712118=30

13^2区域
π(122)=30
π(123)=30
π(124)=30
π(125)=30
π(126)=30
π(127)=30+13^0=31
π(128)=30+13^0=31
π(129)=30+13^0=31
π(130)=30+13^0=31
π(131)=30+13^0.27023815442731974129410800345065=32
π(132)=30+13^0.27023815442731974129410800345065=32
π(133)=30+13^0.27023815442731974129410800345065=32
π(134)=30+13^0.27023815442731974129410800345065=32
π(135)=30+13^0.27023815442731974129410800345065=32
π(136)=30+13^0.27023815442731974129410800345065=32
π(137)=30+13^0.42831734103139468099077437792096=33
π(138)=30+13^0.42831734103139468099077437792096=33
π(139)=30+13^0.54047630885463948258821600690131=34
π(140)=30+13^0.54047630885463948258821600690131=34
π(141)=30+13^0.54047630885463948258821600690131=34
π(142)=30+13^0.54047630885463948258821600690131=34
π(143)=30+13^0.54047630885463948258821600690131=34
π(144)=30+13^0.54047630885463948258821600690131=34
π(145)=30+13^0.54047630885463948258821600690131=34
π(146)=30+13^0.54047630885463948258821600690131=34
π(147)=30+13^0.54047630885463948258821600690131=34
π(148)=30+13^0.54047630885463948258821600690131=34
π(149)=30+13^0.62747356307530335162836969282393=35
π(150)=30+13^0.62747356307530335162836969282393=35
π(151)=30+13^0.69855549545871442228488238137161=36
π(152)=30+13^0.69855549545871442228488238137161=36
π(153)=30+13^0.69855549545871442228488238137161=36
π(154)=30+13^0.69855549545871442228488238137161=36
π(155)=30+13^0.69855549545871442228488238137161=36
π(156)=30+13^0.69855549545871442228488238137161=36
π(157)=30+13^0.75865441295929899467233157578972=37
π(158)=30+13^0.75865441295929899467233157578972=37
π(159)=30+13^0.75865441295929899467233157578972=37
π(160)=30+13^0.75865441295929899467233157578972=37
π(161)=30+13^0.75865441295929899467233157578972=37
π(162)=30+13^0.75865441295929899467233157578972=37
π(163)=30+13^0.81071446328195922388232401035192=38
π(164)=30+13^0.81071446328195922388232401035192=38
π(165)=30+13^0.81071446328195922388232401035192=38
π(166)=30+13^0.81071446328195922388232401035192=38
π(167)=30+13^0.85663468206278936198154875584195=39
π(168)=30+13^0.85663468206278936198154875584195=39
π(169)=30+13^0.85663468206278936198154875584195=39

小草

在π(p^2)=Λ(sk)中sk是震荡的，震荡地趋向于一，只是因为素数的不匀等造成的.设
pk-p(k-1)=d,当d很小时，π(pk^2)-π(p(k-1)^2)的值就小，s就小；当d很大时，
π(pk^2)-π(p(k-1)^2)的值就大，s就大，这就是造成s震荡的根本原因.
我们还可以通过延拓的方法，延拓到所有整数,这时候pk^sk都是不断增加的.

小草

π(2)=1
π(5)=1+2=3
5=(2^2)+1
π(13)=1+2+3=6
13=(3^2)+4
π(31)=1+2+3+5=11
31=(5^2)+6
π(61)=1+2+3+5+7=18
61=(7^2)+12
π(109)=1+2+3+5+7+11=29
109=(11^2)-12
π(181)=1+2+3+5+7+11+13=42
181=(13^2)-12
π(277)=1+2+3+5+7+11+13+17=59
277=(17^2)-12
π(397)=1+2+3+5+7+11+13+17+19=78
397=(19^2)+36
π(547)=1+2+3+5+7+11+13+17+19+23=101
547=(23^2)+18
π(733)=1+2+3+5+7+11+13+17+19+23+29=130
733=(29^2)-108

小草

π(947)=1+2+3+5+7+11+13+17+19+23+29+31=161
947=(31^2)-14
π(1213)=1+2+3+5+7+11+13+17+19+23+29+31+37=198
1213=(37^2)-156
π(1499)=1+2+3+5+7+11+13+17+19+23+29+31+37+41=239
1499=(41^2)-182
π(1831)=1+2+3+5+7+11+13+17+19+23+29+31+37+41+43=282
1831=(43^2)-18
π(2207)=1+2+3+5+7+11+13+17+19+23+29+31+37+41+43+47=329
2207=(47^2)-2
π(2633)=1+2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53=382
2633=(53^2)-176
π(3083)=1+2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59=441
3083=(59^2)-398
π(3583)=1+2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61=502
3583=(61^2)-138
π(4133)=∑p19=569
4133=(67^2)-356
π(4751)=∑p20=640
4751=(71^2)-290