0002１３２人目の素数さん2017/02/12(日) 10:11:59.93ID:Qk9LXaiD
0005１３２人目の素数さん2017/02/12(日) 10:43:05.17ID:Qk9LXaiD
S(n)=n番目の素数
S(m) = | lim[n→∞] [2*3*5*・・・*S(n)]^(1/2+i*y(m))*Σ1/S(k)^(1/2+i*y(m)) | ＝素数のみの無限積*素数のみのゼータ関数
S(m) = | lim[n→∞]√[2*3*5*・・・*S(n)]*{ cos(y(m)*log[2*3*5*・・・*S(n)])+i*sin(y(m)*log[2*3*5*・・・*S(n)]) }*{Σcos(y(m)*log[S(k)]/√S(k)-i*Σsin(y(m)*log[S(k)]/√S(k)) |
S(m) = | lim[n→∞]√[2*3*5*・・・*S(n)]*[ { cos(y(m)*log[2*3*5*・・・*S(n)])*Σcos(y(m)*log[S(k)]/√S(k)+sin(y(m)*log[2*3*5*・・・*S(n)])*Σsin(y(m)*log[S(k)]/√S(k) }
+i*{ sin(y(m)*log[2*3*5*・・・*S(n)])*Σcos(y(m)*log[S(k)]/√S(k)-cos(y(m)*log[2*3*5*・・・*S(n)])*Σsin(y(m)*log[S(k)]/√S(k) } ] |
S(m) = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(m)*log[S(k)]/√S(k)^2+Σsin(y(m)*log[S(k)]/√S(k)^2]
S(1) = 2 = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(1)*log[S(k)]/√S(k)^2+Σsin(y(1)*log[S(k)]/√S(k)^2] ←y(1)≒14.134
S(2) = 3 = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(2)*log[S(k)]/√S(k)^2+Σsin(y(2)*log[S(k)]/√S(k)^2] ←y(2)≒21.022
S(3) = 5 = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(3)*log[S(k)]/√S(k)^2+Σsin(y(3)*log[S(k)]/√S(k)^2] ←y(3)≒25.010
S(4) = 7 = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(4)*log[S(k)]/√S(k)^2+Σsin(y(4)*log[S(k)]/√S(k)^2] ←y(4)≒30.424
S(5) = 11 = lim[n→∞] √[2*3*5*・・・*S(n)]*√[Σcos(y(5)*log[S(k)]/√S(k)^2+Σsin(y(5)*log[S(k)]/√S(k)^2] ←y(5)≒32.935