Fake or Real? : Prime number test...

[1]N is prime(p) or not?

[2]mod(N,6)=c(1,5) is target.but included c(p,!p)

[3]素数判定：約分：c(2:sqrt(N))で、mod()=0, !0

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[4]例）N=375,397,013=(9,923)*(37,831)=p1*p2, sqrt(N)=19375.164...int()=19,375

[5]log6(375397013)=11.01...

[6]x=6 : N=x^11+...+0*x^6+0*x^5+...+5

[7][5]=11/2=5.5; see c(x^5:x^6), x=6 : x^5=7,776, x^6=46,656

[8]素数判定の範囲 : range=c(x^5:int(sqrt(N)))=c(7,776 : 19,375)=(直下A:A)

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[9]x=6は妥当か？：Is x=6 valid?

[10]to be ckecked : x=c(2:10)

[11]x=2 : logx(N)=28.48/2~14 : x^(13,14,15)=c(8192, 16384, 32768) : range=c(16384 : 19375) : diff=2991 : p1=out of range~p1=out;(see [4])

[12]x=3 : logx(N)=17.97/2~8.5 : x^(8,9)=c(6561, 19683) : range=c(6561 : 19375) : diff=12814 : p1 in range~p1=in;

[13]x=4 : logx(N)=14.24/2~7 : x^(6,7,8)=c(4096, 16384, 65536) : range=c(16384 : 19375) : diff=2991 : p1=out;

[14]x=5 : logx(N)=12.26/2~6 : x^(5,6,7)=c(3125, 15625, 78125) : range=c(15625 : 19375) : diff=3750 : p1=out;

[15]x=6 : logx(N)=11.01/2~5.5 : x^(5,6)=c(7776, 46656) : range=c(7776 : 19375) : diff=11599 : p1=in;

[16]x=7 : logx(N)=10.14/2~5 : x^(4,5,6)=c(2401, 16807, 117649) : range=c(16807 : 19375) : diff=2568 : p1=out;

[17]x=8 : logx(N)=9.49/2~4.5 : x^(4,5)=c(4096, 32768) : range=c(4096 : 19375) : diff=15279 : p1=in;

[18]x=9 : logx(N)=8.98/2~4 : x^(3,4,5)=c(729, 6561, 59049) : range=c(6561 : 19375) : diff=12814 : p1=in;

[19]x=10 : logx(N)=8.57/2~4 : x^(3,4,5)=c(1000, 10000, 100000) : range=c(10000 : 19375) : diff=9375 : p1=out;

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[20]in c([11]:[19]) : {p1=in & min(diff)} is x=6

bye.