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[原创]k生素数群的数量公式

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 楼主| 发表于 2010-10-24 15:40 | 显示全部楼层

[原创]k生素数群的数量公式

试着给出30n的偶数在4生素数群中值的分拆公式。4生素数群指(P,P+2,P+6,P+8)这样的素数群,这一组数同时都是素数,每组中的素数间隔距离恒定。中值是指P+4,它是合数,一定有因子5,但P,及P+2,P+6,P+8都是素数。
 楼主| 发表于 2010-11-17 07:58 | 显示全部楼层

[原创]k生素数群的数量公式

上边各楼分别列出了2-12生素数在10^66次方以前的数量,有编程能力的网友可以验证。
 楼主| 发表于 2010-11-29 20:48 | 显示全部楼层

[原创]k生素数群的数量公式

有兴趣的网友可以继续研究k生素数群的中值的2维加法合成,即k生素数群的前后两个素数的中项值相加的分布情况,也可以给出渐进公式。
 楼主| 发表于 2011-4-20 08:04 | 显示全部楼层

[原创]k生素数群的数量公式

k生素数群的数量渐进公式已经找到。只是系数不能全部给出。
发表于 2011-4-20 20:52 | 显示全部楼层

[原创]k生素数群的数量公式

助君成功!
 楼主| 发表于 2011-5-4 06:28 | 显示全部楼层

[原创]k生素数群的数量公式

素数与歌猜,孪生素数对与12n类数的猜想及渐进公式值
 楼主| 发表于 2011-8-19 07:58 | 显示全部楼层

[原创]k生素数群的数量公式

今天浏览此帖时已沉到10页,为了方便感兴趣的网友阅读特顶起。
 楼主| 发表于 2011-11-30 10:41 | 显示全部楼层

[原创]k生素数群的数量公式

p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
2→→→→2→→→→46→→→→6→→→→6→→→→42
6→→→→4→→→→42→→→→12→→→→6→→→→36
8→→→→2→→→→40→→→→16→→→→4→→→→32
12→→→→4→→→→36→→→→18→→→→2→→→→30
18→→→→6→→→→30→→→→22→→→→4→→→→26
20→→→→2→→→→28→→→→28→→→→6→→→→20
26→→→→6→→→→22→→→→30→→→→2→→→→18
30→→→→4→→→→18→→→→36→→→→6→→→→12
32→→→→2→→→→16→→→→40→→→→4→→→→8
36→→→→4→→→→12→→→→42→→→→2→→→→6
42→→→→6→→→→6→→→→46→→→→4→→→→2
48→→→→6→→→→0→→→→48→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
4→→→→4→→→→44→→→→2→→→→2→→→→46
6→→→→2→→→→42→→→→8→→→→6→→→→40
10→→→→4→→→→38→→→→14→→→→6→→→→34
16→→→→6→→→→32→→→→18→→→→4→→→→30
18→→→→2→→→→30→→→→20→→→→2→→→→28
24→→→→6→→→→24→→→→24→→→→4→→→→24
28→→→→4→→→→20→→→→30→→→→6→→→→18
30→→→→2→→→→18→→→→32→→→→2→→→→16
34→→→→4→→→→14→→→→38→→→→6→→→→10
40→→→→6→→→→8→→→→42→→→→4→→→→6
46→→→→6→→→→2→→→→44→→→→2→→→→4
48→→→→2→→→→0→→→→48→→→→4→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→48→→→→0→→→→0→→→→48
4→→→→4→→→→44→→→→2→→→→2→→→→46
6→→→→2→→→→42→→→→12→→→→10→→→→36
10→→→→4→→→→38→→→→14→→→→2→→→→34
16→→→→6→→→→32→→→→18→→→→4→→→→30
18→→→→2→→→→30→→→→20→→→→2→→→→28
24→→→→6→→→→24→→→→24→→→→4→→→→24
28→→→→4→→→→20→→→→30→→→→6→→→→18
30→→→→2→→→→18→→→→32→→→→2→→→→16
34→→→→4→→→→14→→→→38→→→→6→→→→10
36→→→→2→→→→12→→→→42→→→→4→→→→6
46→→→→10→→→→2→→→→44→→→→2→→→→4
48→→→→2→→→→0→→→→48→→→→4→→→→0
以前发表了前12生的排列形式及最短间距和10的66次方内的数量,及系数,这是13生素数的6种不同的排列形式,和最短间距。这样多的排列形式出乎我的意料。
 楼主| 发表于 2011-11-30 11:37 | 显示全部楼层

[原创]k生素数群的数量公式

14生素数的最短间距和排列顺序(即结构式)
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→50→→→→0→→→→0→→→→50
2→→→→2→→→→48→→→→2→→→→2→→→→48
8→→→→6→→→→42→→→→6→→→→4→→→→44
14→→→→6→→→→36→→→→8→→→→2→→→→42
18→→→→4→→→→32→→→→12→→→→4→→→→38
20→→→→2→→→→30→→→→18→→→→6→→→→32
24→→→→4→→→→26→→→→20→→→→2→→→→30
30→→→→6→→→→20→→→→26→→→→6→→→→24
32→→→→2→→→→18→→→→30→→→→4→→→→20
38→→→→6→→→→12→→→→32→→→→2→→→→18
42→→→→4→→→→8→→→→36→→→→4→→→→14
44→→→→2→→→→6→→→→42→→→→6→→→→8
48→→→→4→→→→2→→→→48→→→→6→→→→2
50→→→→2→→→→0→→→→50→→→→2→→→→0
 楼主| 发表于 2011-11-30 13:42 | 显示全部楼层

[原创]k生素数群的数量公式

p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→56→→→→0→→→→0→→→→56
2→→→→2→→→→54→→→→6→→→→6→→→→50
6→→→→4→→→→50→→→→8→→→→2→→→→48
8→→→→2→→→→48→→→→14→→→→6→→→→42
12→→→→4→→→→44→→→→20→→→→6→→→→36
18→→→→6→→→→38→→→→24→→→→4→→→→32
20→→→→2→→→→36→→→→26→→→→2→→→→30
26→→→→6→→→→30→→→→30→→→→4→→→→26
30→→→→4→→→→26→→→→36→→→→6→→→→20
32→→→→2→→→→24→→→→38→→→→2→→→→18
36→→→→4→→→→20→→→→44→→→→6→→→→12
42→→→→6→→→→14→→→→48→→→→4→→→→8
48→→→→6→→→→8→→→→50→→→→2→→→→6
50→→→→2→→→→6→→→→54→→→→4→→→→2
56→→→→6→→→→0→→→→56→→→→2→→→→0
p+n中的n→→相邻间隔→→判断式→→p+n中的n→→相邻间隔→→判断式
0→→→→0→→→→56→→→→0→→→→0→→→→56
2→→→→2→→→→54→→→→2→→→→2→→→→54
6→→→→4→→→→50→→→→6→→→→4→→→→50
12→→→→6→→→→44→→→→12→→→→6→→→→44
14→→→→2→→→→42→→→→14→→→→2→→→→42
20→→→→6→→→→36→→→→20→→→→6→→→→36
24→→→→4→→→→32→→→→26→→→→6→→→→30
26→→→→2→→→→30→→→→30→→→→4→→→→26
30→→→→4→→→→26→→→→32→→→→2→→→→24
36→→→→6→→→→20→→→→36→→→→4→→→→20
42→→→→6→→→→14→→→→42→→→→6→→→→14
44→→→→2→→→→12→→→→44→→→→2→→→→12
50→→→→6→→→→6→→→→50→→→→6→→→→6
54→→→→4→→→→2→→→→54→→→→4→→→→2
56→→→→2→→→→0→→→→56→→→→2→→→→0
以上是15生素数的最短间距和排列顺序(即结构式)

点评

14生素数 50975.35273006145 13生素数 25807.98019260307 15生素数 187823.6870272022  发表于 2021-7-15 18:30
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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}
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\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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