素数の規則を見つけたい。。。

素数の規則を見つけたい。。。 (701ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除ﾚｽ栞

200: １３２人目の素数さん [sage] 2023/11/26(日) 00:24:18.90 ID:5ylX1SN5

x^4 - 2 x^2 y^2 + 2 x^2 z^2 + y^4 + 2 y^2 z^2 + z^4=√((x+y)^2+z^2)^2*√((x-y)^2+z^2)^2*e^(i*arcsin(z/(x+y)))*e^(i*arcsin(-z/(x+y)))*e^(i*arcsin(+z/(x-y)))*e^(i*arcsin(-z/(x-y)))
x^4 - 2 x^2 y^2 + 2 x^2 z^2 + y^4 + 2 y^2 z^2 + z^4=((x+y+i^(2n+1)*z)*(x+y-i^(2n+1)*z)*(x-y+i^(2n+1)*z)*(x-y-i^(2n+1)*z))

x^4 - 2 x^2 y^2 - 2 x^2 z^2 + y^4 - 2 y^2 z^2 + z^4=((x+y+z)*(x+y-z)*(x-y+z)*(x-y-z))*e^(i*arcsin(iz/(x+y)))*e^(i*arcsin(-iz/(x+y)))*e^(i*arcsin(+iz/(x-y)))*e^(i*arcsin(-iz/(x-y)))
x^4 - 2 x^2 y^2 - 2 x^2 z^2 + y^4 - 2 y^2 z^2 + z^4=((x+y+i^2n*z)*(x+y-i^2n*z)*(x-y+i^2n*z)*(x-y-i^2n*z))

x^12 - 2 x^6 y^6 - 2 x^6 z^6 + y^12 - 2 y^6 z^6 + z^12=((x^3+y^3+i^2*z^3)*(x^3+y^3-i^2*z^3)*(x^3-y^3+i^2*z^3)*(x^3-y^3-i^2*z^3))=0
x^12 - 2 x^6 y^6 - 2 x^6 z^6 + y^12 - 2 y^6 z^6 + z^12≠0

cos(2pi*((2*a+1)/2^3-(3*b+1)/3^3-c/5^3-d/7^3)) > cos(2pi*(11^2/210^3))
a = 4 n_1, b = 9 n_2, c = 125 n_3 + 97, d = 343 n_4 + 107,           cos(2pi*((2*4+1)/2^3-(3*9+1)/3^3-97/5^3-107/7^3)) =cos((89 π)/4630500)
a = 4 n_1, b = 3 (3 n_2 + 1), c = 5 (25 n_3 + 22), d = 343 n_4 + 300,  cos(2pi*((2*4+1)/2^3-(3*3+1)/3^3-110/5^3-300/7^3)) =cos((55 π)/4630500) ←110が5を持つため非素数
a = 4 n_1, b = 3 (3 n_2 + 2), c = 125 n_3 + 41, d = 343 n_4 + 32, cos(2pi*((2*3+1)/2^3-(3*6+1)/3^3-41/5^3-32/7^3)) =sin((17 π)/4630500)
a = 4 n_1, b = 9 n_2 + 1, c = 125 n_3 + 31, d = 343 n_4 + 250,    cos(2pi*((2*3+1)/2^3-(3*1+1)/3^3-31/5^3-250/7^3)) =-sin((103 π)/4630500)
a = 4 n_1, b = 9 n_2 + 1, c = 125 n_3 + 74, d = 343 n_4 + 132, 　cos(2pi*((2*3+1)/2^3-(3*1+1)/3^3-74/5^3-132/7^3)) =sin((113 π)/4630500)

http://rio2016.5ch.net/test/read.cgi/math/1640355175/200

359: １３２人目の素数さん [sage] 2024/01/07(日) 00:36:17.90 ID:SsbMX1Ts

1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
43個

121, 143, 169, 187, 209   ←11以上の素数の積

43+5=48=(2^1-2^0)*(3^1-3^0)*(5^1-5^0)*(7^1-7^0)

e^(i*2π*1/(210))+e^(i*2π*11/(210))+e^(i*2π*13/(210))+e^(i*2π*17/(210))+e^(i*2π*19/(210))+e^(i*2π*23/(210))+e^(i*2π*29/(210))+e^(i*2π*31/(210))
+e^(i*2π*37/(210))+e^(i*2π*41/(210))+e^(i*2π*43/(210))+e^(i*2π*47/(210))+e^(i*2π*53/(210))+e^(i*2π*59/(210))+e^(i*2π*61/(210))+e^(i*2π*67/(210))
+e^(i*2π*71/(210))+e^(i*2π*73/(210))+e^(i*2π*79/(210))+e^(i*2π*83/(210))+e^(i*2π*89/(210))+e^(i*2π*97/(210))+e^(i*2π*101/(210))+e^(i*2π*103/(210))
+e^(i*2π*107/(210))+e^(i*2π*109/(210))+e^(i*2π*113/(210))+e^(i*2π*121/(210))+e^(i*2π*127/(210))+e^(i*2π*131/(210))+e^(i*2π*137/(210))+e^(i*2π*139/(210))
+e^(i*2π*143/(210))+e^(i*2π*149/(210))+e^(i*2π*151/(210))+e^(i*2π*157/(210))+e^(i*2π*163/(210))+e^(i*2π*167/(210))+e^(i*2π*169/(210))+e^(i*2π*173/(210))
+e^(i*2π*179/(210))+e^(i*2π*181/(210))+e^(i*2π*187/(210))+e^(i*2π*191/(210))+e^(i*2π*193/(210))+e^(i*2π*197/(210))+e^(i*2π*199/(210))+e^(i*2π*209/(210))

http://rio2016.5ch.net/test/read.cgi/math/1640355175/359

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