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)
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176: １３２人目の素数さん [sage] 2023/09/16(土) 11:52:44.16 ID:PJtUNqdO

素数を式で出すには定義から見つけないと無理だな虚数みたいに
((-((-((1/5-1/6)-1/7)-1/11)-1/13)+1/17)-1/19-1/23)-1/29+1/31=3770006491/200560490130
((-((-((1/5-1/6)-1/7)-1/11)-1/13)+1/17)-1/19-1/23)-1/29+1/31-1/37=-61070249963/7420738134810
((-((-((1/5-1/6)-1/7)-1/11)-1/13)+1/17)-1/19-1/23)-1/29+1/31-1/37+1/41=4916857886327/304250263527210
4916857886327=1301*3779291227
4916857886327は2から41の素数で割れないものの43以上の素数の積になる可能性がある

cos(2pi*(1/2+n/(3*5*7*11*13*17))) >cos(2pi*(19^2/510510))
255255m+127447<((1/3-1/5+1/7-1/11+1/13-1/17)*3*5*7*11*13*17)<255255m+127808のとき
-278/935<m<-75533/255255のとき255255m+127447<n<255255m+127808の範囲内の整数nは3,5,7,11,13,17で割れない整数
ｍが整数にならないので((1/3-1/5+1/7-1/11+1/13-1/17)*3*5*7*11*13*17)は3.5.7.11.13.17で割れないものの
255255m+127447<((1/3-1/5+1/7-1/11+1/13-1/17)*3*5*7*11*13*17)<255255m+127808は満たさない

255255m+121275537447<n<255255m+127808　かつnが3.5.7.11.13.17を素因数に持たない数
127553=229*557
cos(2pi*(1/2+127553/(3*5*7*11*13*17))) =cos((149 π)/255255)
127559=199*641
cos(2pi*(1/2+127559/(3*5*7*11*13*17)))=cos((137 π)/255255)

http://rio2016.5ch.net/test/read.cgi/math/1640355175/176

177: １３２人目の素数さん [sage] 2023/09/16(土) 21:42:29.39 ID:PJtUNqdO

255255m+127447<X＝((1/3+n/(5*7*11*13*17))*3*5*7*11*13*17)<255255m+127808
255255 m + 127447<3 n + 85085<255255 m + 127808

42362/3<n<14241

cos(2pi*(1/2+X/(3*5*7*11*13*17)))
e^(i*2pi*(1/2+((1/3+n/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) ←nが42362/3<n<14241のとき分子は素数になる

e^(i*2pi*(1/2+((1/3+14130/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(61 i π)/51051)
e^(i*2pi*(1/2+((1/3+14131/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(23 i π)/19635)
e^(i*2pi*(1/2+((1/3+14132/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(293 i π)/255255)
e^(i*2pi*(1/2+((1/3+14133/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(41 i π)/36465)
e^(i*2pi*(1/2+((1/3+14134/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(281 i π)/255255)
e^(i*2pi*(1/2+((1/3+14135/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(5 i π)/4641)
e^(i*2pi*(1/2+((1/3+14136/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(269 i π)/255255)
e^(i*2pi*(1/2+((1/3+14137/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(263 i π)/255255)
e^(i*2pi*(1/2+((1/3+14138/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^(-(257 i π)/255255)

e^(i*2pi*(1/2+((1/3+14238/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^((49 i π)/36465) 14238が７を素因数にもつため分子が素数にならない
e^(i*2pi*(1/2+((1/3+14239/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^((349 i π)/255255)
e^(i*2pi*(1/2+((1/3+14240/(5*7*11*13*17))*3*5*7*11*13*17)/(3*5*7*11*13*17))) =e^((71 i π)/51051)

http://rio2016.5ch.net/test/read.cgi/math/1640355175/177

178: １３２人目の素数さん [sage] 2023/09/16(土) 22:15:04.58 ID:PJtUNqdO

e^(i*2pi*(1/2+X1/(3*5)))
cos(2pi*(1/2+((1/2+n/3)*(2*3))/(3*5)))>cos(2π*49/30)を満たすとき分子は素数
1/2 (15 m - 16)<n<5/2 (3 m - 1)

e^(i*2pi*(1/2+(1/2+((1/2+n/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))
cos(2pi*(1/2+(1/2+((1/2+n/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))>cos(2π*121/210)を満たすとき分子は素数

nが1/4 (105 m - 118)<n<1/4 (105 m - 29)をみたしかつ3または7の倍数でないとき分子が素数

e^(i*2pi*(1/2+(1/2+((1/2+n/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))
e^(i*2pi*(1/2+(1/2+((1/2-8/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((83 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-10/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((67 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-11/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((59 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-13/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((43 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-14/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((35 i π)/105) ←非素数
e^(i*2pi*(1/2+(1/2+((1/2-16/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((19 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-17/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((11 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-19/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((5 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-20/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((-13 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-22/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((-29 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-23/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^((-37 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-25/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^(-(53 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-26/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^(-(61 i π)/105)
e^(i*2pi*(1/2+(1/2+((1/2-28/3)*(2*3))/(3*5))*(2*3*5)/(3*5*7)))=e^(-(77 i π)/105)　←非素数

http://rio2016.5ch.net/test/read.cgi/math/1640355175/178

179: １３２人目の素数さん [sage] 2023/09/16(土) 23:51:32.96 ID:PJtUNqdO

e^(i*2pi*(1/2+(1/2+((1/2+(1/2+n/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11)))
1/8 (1155 m - 809)<n<5/8 (231 m - 128)を満たしかつ3の倍数でないとき分子が素数（非素数が混じる

e^(i*2pi*(1/2+(1/2+((1/2+(1/2-82/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((137 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-83/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((121 i π)/1155)　←非素数
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-85/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((89 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-86/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((73 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-88/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((41 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-89/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((25 i π)/1155)　←非素数
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-91/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-7 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-92/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-23 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-94/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-55 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-95/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-71 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-97/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-103 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-98/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11))) =e^((-119 i π)/1155) ←非素数
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-100/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11)))=e^((-151 i π)/1155)
e^(i*2pi*(1/2+(1/2+((1/2+(1/2-101/3)*(2*3)/(3*5))*(2*3*5))/(3*5*7))*(2*3*5*7)/(3*5*7*11)))=e^((-167 i π)/1155)

http://rio2016.5ch.net/test/read.cgi/math/1640355175/179

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