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数论问题巅峰对决

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 楼主| 发表于 2020-8-9 11:22 | 显示全部楼层
无缝连接:
44058/44064/44070/44076/44082/44088/44094/44100/44106/44112/44118/44124/44130/44136/44142/44148/44154/44160/44166/44172/
44178/44184/44190/44196/44202/44208/44214/44220/44226/44232/44238/44244/44250/44256/44262/44268/44274/44280/44286/44292/
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49098/49104/49110/49116/49122/49128/49134/49140/49146/49152/49158/49164/49170/49176/49182/49188/49194/49200/49206/49212/
49218/49224/49230/49236/49242/49248/49254/49260/49266/49272/49278/49284/49290/49296/49302/49308/49314/49320/49326/49332/
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49578/49584/49590/49596/49602/49608/49614/49620/49626/49632/49638/49644/49650/49656/49662/49668/49674/49680/49686/49692/
49698/49704/49710/49716/49722/49728/49734/49740/49746/49752/49758/49764/49770/49776/49782/49788/49794/49800/49806/49812/
49818/49824/49830/49836/49842/49848/49854/49860/49866/49872/49878/49884/49890/49896/49902/49908/49914/49920/49926/49932/
49938/49944/49950/49956/49962/49968/49974/49980/49986/49992/49998/50004/50010/50016/50022/50028/50034/50040/50046/50052/
50058/50064/50070/50076/50082/50088/50094/50100/50106/50112/50118/50124/50130/50136/50142/50148/50154/50160/50166/50172/
50178/50184/50190/50196/50202/50208/50214/50220/50226/50232/50238/50244/50250/50256/50262/50268/50274/50280/50286/50292/
50298/50304/50310/50316/50322/50328/50334/50340/50346/50352/50358/50364/50370/50376/50382/50388/50394/50400/50406/50412/
50418/50424/50430/50436/50442/50448/50454/50460/50466/50472/50478/50484/50490/50496/50502/50508/50514/50520/50526/50532/
50538/50544/50550/50556/50562/50568/50574/50580/50586/50592/50598/50604/50610/50616/50622/50628/50634/50640/50646/50652/

后面还很多不发了,而20000~40000内并没有实现偶数全覆盖。继续算也不可能实现到某数后偶数全覆盖了。能覆盖大于等于1122的差为6的全体偶数。
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 楼主| 发表于 2020-8-9 11:28 | 显示全部楼层
而孪中p+3的和,能覆盖大于等于8014的全体偶数。
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 楼主| 发表于 2020-8-9 11:50 | 显示全部楼层
额,您的命题成立,非常有趣,比哥德巴赫猜想和孪生素数猜想更厉害,虽然我证明不了我确信是成立的,佩服!
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发表于 2020-8-9 12:24 | 显示全部楼层
本帖最后由 蔡家雄 于 2020-8-9 16:14 编辑

再三谢谢 ysr,辛苦您了!

2生素数( p, p+6 )遍历覆盖 对称4生连续素数15x±2, 15x±4,  及

2生素数( p, p+6 )遍历覆盖 对称6生连续素数15x±2, 15x±4, 15x±8 ,
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 楼主| 发表于 2020-8-9 12:58 | 显示全部楼层
命题很好!感谢沟通探讨,不过我不懂啥是k生素数没有研究那个。
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 楼主| 发表于 2020-8-9 13:00 | 显示全部楼层
本帖最后由 ysr 于 2020-8-9 05:25 编辑

下面是改进版素数程序计算结果:(这个结果还是低于实际的)
10^5内的素数个数下限为 9571
10^6内的素数个数下限为 78415
10^7内的素数个数下限为 663567
10^8内的素数个数下限为 5749881
10^9内的素数个数下限为 50720963
10^10内的素数个数下限为 453678357
10^11内的素数个数下限为 4104048399
10^12内的素数个数下限为 37379740471
10^13内的素数个数下限为 339143631050
10^14内的素数个数下限为 3127108390065
10^15内的素数个数下限为 29161705875438
10^16内的素数个数下限为 273844893009129
10^17内的素数个数下限为 2.58444344177065E+15
10^18内的素数个数下限为 2.44905566203191E+16
10^19内的素数个数下限为 2.32899659565197E+17
10^20内的素数个数下限为 2.22186121705457E+18
10^21内的素数个数下限为 2.12577130696508E+19
10^22内的素数个数下限为 2.03921097636325E+20
10^23内的素数个数下限为 1.96093429480603E+21
10^24内的素数个数下限为 1.88990491098466E+22
10^25内的素数个数下限为 1.82525287620363E+23
10^26内的素数个数下限为 1.76624225909695E+24
10^27内的素数个数下限为 1.7122462099504E+25
10^28内的素数个数下限为 1.66272744579784E+26
10^29内的素数个数下限为 1.61722279682205E+27

程序代码如下:(仅发主程序)
Private Sub Command1_Click()
Dim a, b, c
a = Trim(Text1)
Do While Log(a) / Log(10) < 28
a = MbC(Trim(a), 10)
b = Sqr(a)
c = a / Log(a)
If a > 10 ^ 11 Then
s = 1
Do While Int(b ^ (2 ^ (1 - s))) > 1
b6 = b ^ (2 ^ (1 - s))
b7 = 2 ^ (s + 14) * b6 + b7
Print b7
s = s + 1
Loop
c = (a + b7) / Log(a)
ElseIf a > 10000000 Then
a1 = Log(a) / Log(10)
b2 = Exp(1.033 * a1)
B1 = 0.159 * b2
b4 = (1.74136140824861 ^ (1.8 * a1)) / 4.9
b5 = (B1 + b4) / 2
c = (a + (b5 + 4) * b) / Log(a)
ElseIf a >= 10000 Then
a1 = Log(a) / Log(10)
b3 = (56 * a1 ^ 3 - 741 * a1 ^ 2 + 3367 * a1 - 5142) / 6
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a >= 1000 Then
c = (a + 4 * b) / Log(a)
ElseIf a > 500 Then
c = (a + 2 * b) / Log(a)
Else
c = c
End If
d = a / c
D1 = Int(c) * d
a1 = Log(a) / Log(10)
js = 0.0002 * a1 ^ 2 - 0.0035 * a1 + 1.0132
c = c * js
Text2 = Text2 & "10^" & Log(a) / Log(10) & "内的素数个数下限为 " & Int(c) & vbCrLf
Loop
Text3 = D1
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
End Sub
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 楼主| 发表于 2020-8-9 13:12 | 显示全部楼层
本帖最后由 ysr 于 2020-8-9 05:17 编辑

另一个素数个数程序计算结果:(这个结果大于实际了)
10^10内的素数个数下限为 459632260
10^11内的素数个数下限为 4124591238
10^12内的素数个数下限为 37057215852
10^13内的素数个数下限为 347036109068
10^14内的素数个数下限为 3307240726260
10^15内的素数个数下限为 32015266593043
10^16内的素数个数下限为 314225663596112
10^17内的素数个数下限为 3.12114619331356E+15
10^18内的素数个数下限为 3.13181093186547E+16
10^19内的素数个数下限为 3.16924208102884E+17
10^20内的素数个数下限为 3.22944115072979E+18
10^21内的素数个数下限为 3.30915725553855E+19
10^22内的素数个数下限为 3.4056927094738E+20
10^23内的素数个数下限为 3.51675616282711E+21
10^24内的素数个数下限为 3.64035167148443E+22
10^25内的素数个数下限为 3.77469845804351E+23
10^26内的素数个数下限为 3.91818032233073E+24
10^27内的素数个数下限为 4.06932547868719E+25
10^28内的素数个数下限为 4.22681649296179E+26
10^29内的素数个数下限为 4.38952570551729E+27

程序代码如下:(仅发主程序)
Private Sub Command1_Click()
Dim a, b, c
a = Trim(Text1)
Do While Log(a) / Log(10) < 28
a = MbC(Trim(a), 10)
b = Sqr(a)
c = a / Log(a)
If a > 10 ^ 11 Then
a1 = Log(a) / Log(10)
b3 = (1.74136140824861 ^ ((1.06415 * Exp(-0.00175 * (a1 - 0.65 * (a1 - 21)))) ^ a1)) ^ a1
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a > 10000000 Then
a1 = Log(a) / Log(10)
b2 = Exp(1.033 * a1)
B1 = 0.159 * b2
b4 = (1.74136140824861 ^ (1.8 * a1)) / 4.9
b5 = (B1 + b4) / 2
c = (a + (b5 + 4) * b) / Log(a)
ElseIf a >= 10000 Then
a1 = Log(a) / Log(10)
b3 = (56 * a1 ^ 3 - 741 * a1 ^ 2 + 3367 * a1 - 5142) / 6
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a >= 1000 Then
c = (a + 4 * b) / Log(a)
ElseIf a > 500 Then
c = (a + 2 * b) / Log(a)
Else
c = c
End If
d = a / c
D1 = Int(c) * d
a1 = Log(a) / Log(10)
js = 0.0059 * a1 ^ 2 - 0.1313 * a1 + 1.7343
c = c * js
Text2 = Text2 & "10^" & Log(a) / Log(10) & "内的素数个数下限为 " & Int(c) & vbCrLf
Loop
Text3 = D1
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
End Sub
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发表于 2020-8-9 13:15 | 显示全部楼层
请 ysr 编程寻找:对称6生连续素数15x±2, 15x±4, 15x±8 ,

注:15x 就是这6个连续素数的中项 ( 孪中数 ),分别:加减2,加减4,加减8,
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 楼主| 发表于 2020-8-9 13:29 | 显示全部楼层
抱歉!休息一会儿,下午去上班呢,明天下午再弄吧,抱歉啊!
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 楼主| 发表于 2020-8-10 19:23 | 显示全部楼层
“对称6生连续素数15x±2, 15x±4, 15x±8 ,”是指中间没有其他素数还是不用管中间是否有其他素数?其中15x+2,与15x+4是孪生素数吧就是说x相同?
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\frac{\square}{\square}\sqrt{\square}\square_{\baguet}^{\baguet}\overarc{\square}\ \dot{\baguet}\left(\square\right)\binom{\square}{\square}\begin{cases}\square\\\square\end{cases}\ \begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\to\Rightarrow\mapsto\alpha\ \theta\ \pi\times\div\pm\because\angle\ \infty
\frac{\square}{\square}\sqrt{\square}\sqrt[\baguet]{\square}\square_{\baguet}\square^{\baguet}\square_{\baguet}^{\baguet}\sum_{\baguet}^{\baguet}\prod_{\baguet}^{\baguet}\coprod_{\baguet}^{\baguet}\int_{\baguet}^{\baguet}\lim_{\baguet}\lim_{\baguet}^{\baguet}\bigcup_{\baguet}^{\baguet}\bigcap_{\baguet}^{\baguet}\bigwedge_{\baguet}^{\baguet}\bigvee_{\baguet}^{\baguet}
\underline{\square}\overline{\square}\overrightarrow{\square}\overleftarrow{\square}\overleftrightarrow{\square}\underrightarrow{\square}\underleftarrow{\square}\underleftrightarrow{\square}\dot{\baguet}\hat{\baguet}\vec{\baguet}\tilde{\baguet}
\left(\square\right)\left[\square\right]\left\{\square\right\}\left|\square\right|\left\langle\square\right\rangle\left\lVert\square\right\rVert\left\lfloor\square\right\rfloor\left\lceil\square\right\rceil\binom{\square}{\square}\boxed{\square}
\begin{cases}\square\\\square\end{cases}\begin{matrix}\square&\square\\\square&\square\end{matrix}\begin{pmatrix}\square&\square\\\square&\square\end{pmatrix}\begin{bmatrix}\square&\square\\\square&\square\end{bmatrix}\begin{Bmatrix}\square&\square\\\square&\square\end{Bmatrix}\begin{vmatrix}\square&\square\\\square&\square\end{vmatrix}\begin{Vmatrix}\square&\square\\\square&\square\end{Vmatrix}\begin{array}{l|l}\square&\square\\\hline\square&\square\end{array}
\to\gets\leftrightarrow\nearrow\searrow\downarrow\uparrow\updownarrow\swarrow\nwarrow\Leftarrow\Rightarrow\Leftrightarrow\rightharpoonup\rightharpoondown\impliedby\implies\Longleftrightarrow\leftharpoonup\leftharpoondown\longleftarrow\longrightarrow\longleftrightarrow\Uparrow\Downarrow\Updownarrow\hookleftarrow\hookrightarrow\mapsto
\alpha\beta\gamma\Gamma\delta\Delta\epsilon\varepsilon\zeta\eta\theta\Theta\iota\kappa\varkappa\lambda\Lambda\mu\nu\xi\Xi\pi\Pi\varpi\rho\varrho\sigma\Sigma\tau\upsilon\Upsilon\phi\Phi\varphi\chi\psi\Psi\omega\Omega\digamma\vartheta\varsigma\mathbb{C}\mathbb{H}\mathbb{N}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{Z}\Re\Im\aleph\partial\nabla
\times\cdot\ast\div\pm\mp\circ\backslash\oplus\ominus\otimes\odot\bullet\varnothing\neq\equiv\not\equiv\sim\approx\simeq\cong\geq\leq\ll\gg\succ\prec\in\ni\cup\cap\subset\supset\not\subset\not\supset\notin\not\ni\subseteq\supseteq\nsubseteq\nsupseteq\sqsubset\sqsupset\sqsubseteq\sqsupseteq\sqcap\sqcup\wedge\vee\neg\forall\exists\nexists\uplus\bigsqcup\bigodot\bigotimes\bigoplus\biguplus\bigcap\bigcup\bigvee\bigwedge
\because\therefore\angle\parallel\perp\top\nparallel\measuredangle\sphericalangle\diamond\diamondsuit\doteq\propto\infty\bowtie\square\smile\frown\bigtriangledown\triangle\triangleleft\triangleright\bigcirc \wr\amalg\models\preceq\mid\nmid\vdash\dashv\nless\ngtr\ldots\cdots\vdots\ddots\surd\ell\flat\sharp\natural\wp\clubsuit\heartsuit\spadesuit\oint\lfloor\rfloor\lceil\rceil\lbrace\rbrace\lbrack\rbrack\vert\hbar\aleph\dagger\ddagger

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