[原创]k生素数群的数量公式

白新岭 · 发表于 2019-7-28 16:32

最密38生素数的最终系数C38(L176)=1140136862852420000.0 （这是88#第一行所示的38生素数的系数）

白新岭 · 发表于 2019-7-28 16:34

n(10的次幂）最密38生素数的数量
65 3.000000000000000000E+00
66 1.800000000000000000E+01
67 1.060000000000000000E+02
68 6.010000000000000000E+02
69 3.438000000000000000E+03
70 1.981100000000000000E+04
71 1.150540000000000000E+05
72 6.733230000000000000E+05
73 3.969972000000000000E+06
74 2.357789400000000000E+07
75 1.410231590000000000E+08
76 8.493005840000000000E+08
77 5.149190095000000000E+09
78 3.142295464800000000E+10
79 1.929801861040000000E+11
80 1.192520479549000000E+12
81 7.413765798382000000E+12
82 4.636249080980200000E+13
83 2.915996017448320000E+14
84 1.844331691160580000E+15
85 1.172910583917670000E+16
86 7.499088192529000000E+16
87 4.819650786456590000E+17
88 3.113393341278820000E+18
89 2.021218517384690000E+19
90 1.318574456514720000E+20
91 8.642931169395650000E+20
92 5.691633289597120000E+21
93 3.765201087671970000E+22
94 2.501913121450180000E+23
95 1.669735969476680000E+24
96 1.119115634456950000E+25
97 7.532081547455620000E+25
98 5.090148634566790000E+26
99 3.453702927338860000E+27
100 2.352574181573190000E+28
101 1.608686208618090000E+29
102 1.104169801297350000E+30
103 7.606847950853170000E+30
104 5.259527371873440000E+31
105 3.649484236481210000E+32
106 2.541145878517480000E+33
107 1.775466227548010000E+34
108 1.244664016092570000E+35
109 8.754305815748120000E+35
110 6.177245524171720000E+36
111 4.372663028479580000E+37
112 3.104919010095010000E+38
113 2.211482212851790000E+39
114 1.579872238819570000E+40
115 1.131990766423250000E+41
116 8.134368766567690000E+41
117 5.861963662624650000E+42
118 4.236229451532220000E+43
119 3.069815348733870000E+44
120 2.230598031471640000E+45
121 1.625125942203550000E+46
122 1.187107996319440000E+47
123 8.693852351305610000E+47
124 6.383147690193430000E+48

白新岭 · 发表于 2019-7-28 16:44

最密39生素数的最终系数C39(L182)=5405212945308910000.0 （这是90#第一行所示的39生素数的系数）

白新岭 · 发表于 2019-7-28 16:46

n(10的次幂）最密39生素数的数量
67 3.000000000000000000E+00
68 1.800000000000000000E+01
69 1.030000000000000000E+02
70 5.870000000000000000E+02
71 3.363000000000000000E+03
72 1.940800000000000000E+04
73 1.128490000000000000E+05
74 6.610690000000000000E+05
75 3.900719000000000000E+06
76 2.317966800000000000E+07
77 1.386926120000000000E+08
78 8.354204260000000000E+08
79 5.065094676000000000E+09
80 3.090499623800000000E+10
81 1.897401037730000000E+11
82 1.171958235269000000E+12
83 7.281542906341000000E+12
84 4.550205626098800000E+13
85 2.859402225683330000E+14
86 1.806751836463400000E+15
87 1.147744490884480000E+16
88 7.329287340835320000E+16
89 4.704313993542590000E+17
90 3.034581707785020000E+18
91 1.967075317046320000E+19
92 1.281197265843950000E+20
93 8.383756463336850000E+20
94 5.511187473077150000E+21
95 3.639093728807530000E+22
96 2.413469508323230000E+23
97 1.607500767505760000E+24
98 1.075184199891780000E+25
99 7.221036974977210000E+25
100 4.869284031118980000E+26
101 3.296434235087520000E+27
102 2.240285986092820000E+28
103 1.528302145855190000E+29
104 1.046476884122220000E+30
105 7.191733445237980000E+30
106 4.960104362752340000E+31
107 3.432985411044520000E+32
108 2.384231721528860000E+33
109 1.661470258079480000E+34
110 1.161655353346720000E+35
111 8.148476031611270000E+35
112 5.734087507168080000E+36
113 4.047773645901720000E+37
114 2.866209355051020000E+38
115 2.035709659616130000E+39
116 1.450163829045810000E+40
117 1.036070390950610000E+41
118 7.423533184584360000E+41
119 5.334086244003780000E+42
120 3.843410085773310000E+43
121 2.776902138290520000E+44
122 2.011740350056130000E+45
123 1.461273844333030000E+46
124 1.064194292991160000E+47
125 7.770010812281260000E+47
126 5.687427775679470000E+48

白新岭 · 发表于 2019-7-28 16:50

39生素数以后的素数式没有现成的。
有了素数式很容易得到的k生素数的系数和其数量。

白新岭 · 发表于 2019-7-29 19:55

最密40生素数的最终系数C40(L186)=28206299375439800000.0

白新岭 · 发表于 2019-7-29 19:58

n(10的次幂）最密40生素数的数量
69 3.000000000000000000E+00
70 1.900000000000000000E+01
71 1.080000000000000000E+02
72 6.150000000000000000E+02
73 3.531000000000000000E+03
74 2.040200000000000000E+04
75 1.187680000000000000E+05
76 6.963930000000000000E+05
77 4.112149000000000000E+06
78 2.444913700000000000E+07
79 1.463396600000000000E+08
80 8.816383210000000000E+08
81 5.345368367000000000E+09
82 3.261032261800000000E+10
83 2.001505859590000000E+11
84 1.235718058299000000E+12
85 7.673286404269000000E+12
86 4.791636024884400000E+13
87 3.008635800487550000E+14
88 1.899257142528570000E+15
89 1.205238859704720000E+16
90 7.687521645407250000E+16
91 4.928035503485720000E+17
92 3.174589560015380000E+18
93 2.054855188173030000E+19
94 1.336318093823260000E+20
95 8.730317044174970000E+20
96 5.729274760342740000E+21
97 3.776400130667630000E+22
98 2.499917025145990000E+23
99 1.661897190159250000E+24
100 1.109370415066880000E+25
101 7.435443697107150000E+25
102 5.003341798913510000E+26
103 3.379889875696140000E+27
104 2.291928872840470000E+28
105 1.559997829878450000E+29
106 1.065712616770250000E+30
107 7.306667391934580000E+30
108 5.027272172103690000E+31
109 3.470969643278410000E+32
110 2.404622489080060000E+33
111 1.671451340960920000E+34
112 1.165641815733700000E+35
113 8.155217603957080000E+35
114 5.723744366009630000E+36
115 4.029721068941780000E+37
116 2.845747074451090000E+38
117 2.015678433274900000E+39
118 1.431948874466620000E+40
119 1.020218819809160000E+41
120 7.289495906440640000E+41
121 5.222991681906370000E+42
122 3.752655371471770000E+43
123 2.703559155810170000E+44
124 1.952952738583040000E+45
125 1.414449787160250000E+46
126 1.027081749879220000E+47
127 7.476981994591290000E+47
128 5.456750445026990000E+48

白新岭 · 发表于 2019-7-30 15:31

0,2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,6,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4
0,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,6,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4,2
0,2,4,6,2,6,6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,6,4,2,4
0,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,10,2,4,6,2,6,4,2,4,2
0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,10,2,4,6,2,6,4,2,16,2,16,2,4,6,2,6,4,2,4,6,6,2,6,4,2
0,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,10,2,4,6,8,4,2,4,2
0,2,4,2,4,8,6,4,2,10,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4
0,2,4,6,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4
0,4,6,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2
0,2,4,6,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4
0,4,6,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4,2
0,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,10,2,16,2,16,2,4,6,2,6,4,2,4,6,6,2,6,4,2
0,2,4,2,4,14,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4
0,4,2,4,14,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2
0,2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,14,4,2,4
0,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,14,4,2,4,2
0,2,4,6,2,6,6,4,2,4,6,2,6,4,2,16,2,16,2,10,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4
0,2,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,6,4
0,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,6,4,2
0,2,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,6,4
0,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,6,4,2
0,4,2,4,6,2,6,4,2,4,6,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,10,2,4,6,8,4,2,4,2
0,2,4,2,4,8,6,4,2,10,6,2,6,4,8,4,6,8,4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4
0,2,4,6,2,6,6,4,2,4,6,2,6,4,2,16,2,16,2,4,6,2,6,4,2,10,6,2,6,4,2,6,4,6,8,4,2,4,2,4
0,2,4,2,4,6,2,6,4,2,10,6,2,6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,6,2,6,6,4,2,4,6,8,4,2,4
0,4,2,4,6,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,12,4,2,4,8,6,4,2,4,6,6,2,6,4,2
0,2,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,6,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4
0,4,2,4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,6,6,4,8,6,4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,4,2
这是最密40生素数的邻距表示形式，有28种，总间距为186，以上两楼的数据是其中的一种最密40生素数的。

白新岭 · 发表于 2019-7-30 16:22

素数式41 素数式41 素数式41 素数式41 素数式41 素数式41 素数式41 素数式41
0 0 0 0 0 0 0 0
2 2 2 2 2 2 2 2
4 4 4 4 4 4 4 4
2 2 6 2 6 2 2 2
4 4 6 4 8 4 4 4
6 6 2 6 6 8 14 8
2 2 6 2 4 6 4 6
6 6 4 6 2 4 2 4
4 4 2 4 4 2 4 2
2 2 4 2 6 4 6 4
4 4 6 4 6 6 6 6
6 6 6 6 2 6 2 6
6 6 2 6 6 2 6 2
2 2 6 2 4 6 4 6
6 6 6 6 8 4 8 4
6 6 6 6 4 8 4 8
6 6 4 6 6 4 6 4
4 4 6 4 8 6 8 6
6 6 8 6 4 8 4 8
8 8 4 8 2 4 2 6
4 4 6 4 6 2 6 6
6 6 2 6 4 6 4 4
6 2 4 2 8 4 8 8
8 4 8 4 6 8 6 6
6 8 6 8 4 6 4 4
4 6 4 6 6 4 6 6
8 4 8 4 6 6 6 6
4 8 4 8 6 6 6 6
6 4 6 4 2 6 2 2
2 6 2 6 6 2 6 6
6 2 6 2 6 6 6 6
6 6 6 6 4 6 4 4
4 6 4 6 2 4 2 2
2 4 2 4 4 2 4 4
4 2 4 2 6 4 6 6
6 4 6 4 2 6 2 2
8 14 8 6 6 2 6 6
4 4 4 8 4 6 4 4
2 2 2 6 2 6 2 2
4 4 4 4 4 4 4 4
2 2 2 2 2 2 2 2
这是最密41生素数的邻距表示形式，共8种，总间距188.

白新岭 · 发表于 2019-7-30 16:46

最密41生素数的最终系数C41(L188)=119308778811593000000.0 (上楼第一列的41生素数系数）

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[原创]k生素数群的数量公式

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