World!Of
Numbers

WON plate
230 |

[ May 22, 2024 ] [ Last update ]
Manually searching for Sums of Five Fifthpowers ⩽ 1000
By Patrick De Geest

 ∑ = 5 + 5 + 5 + 5 + 5 ⯇ +/- ⯈ ⯇ +/- ⯈ ⯇ +/- ⯈ ⯇ +/- ⯈ ⯇ +/- ⯈ random random random random random Randomize first four terms and adjust last one random scope

If you find a solution that is not present in this list of Sums of Five Fifthpowers
please mail me the new find and will add it to the list.

Following is some Pari/GP code that automates the search for these sums of five fifthpowers.
Lowering the random scope value results in finding smaller solutions much sooner. Using
higher random scope values will make a find much rarer but more satisfying.

 ``` \\ This is my PARI/GP program code for WONplate 230 by PDG [May 23, 2024] → rnd5pow.gp f="D:/Teksten2024/Random-so5p.txt"; { scope=1500; print("Random between -",scope," and +",scope," limit up to 1000"); print(); write(f, "Random between -",scope," and +",scope," limit up to 1000"); write(f,); while(1==1, y=round(random(0.1)*scope*2-scope); x=round(random(0.1)*scope*2-scope); w=round(random(0.1)*scope*2-scope); v=round(random(0.1)*scope*2-scope); s4p=v^5+w^5+x^5+y^5; z=round(sqrtn(abs(s4p),5)); z=-1*sign(s4p)*z; n=s4p+z^5; if(v+w==0||v+x==0||v+y==0||v+z==0||w+x==0||w+y==0||w+z==0||x+y==0||x+z==0||y+z==0, n=99999); if(abs(n)<=1000, a=[v,w,x,y,z]; if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[3])>abs(a[4]),sw=a[3];a[3]=a[4];a[4]=sw); if(abs(a[4])>abs(a[5]),sw=a[4];a[4]=a[5];a[5]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[3])>abs(a[4]),sw=a[3];a[3]=a[4];a[4]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); if(abs(a[2])>abs(a[3]),sw=a[2];a[2]=a[3];a[3]=sw); if(abs(a[1])>abs(a[2]),sw=a[1];a[1]=a[2];a[2]=sw); vv=a[1];ww=a[2];xx=a[3];yy=a[4];z=a[5]; print1(n," = "); if(vv<0, print1("(",vv,")"), print1(vv)); print1("^5+"); if(ww<0, print1("(",ww,")"), print1(ww)); print1("^5+"); if(xx<0, print1("(",xx,")"), print1(xx)); print1("^5+"); if(yy<0, print1("(",yy,")"), print1(yy)); print1("^5+"); if(z<0, print1("(",z,")"), print1(z)); print1("^5"); print; write1(f, n," = "); if(vv<0, write1(f, "(",vv,")"), write1(f, vv)); write1(f, "^5+"); if(ww<0, write1(f, "(",ww,")"), write1(f, ww)); write1(f, "^5+"); if(xx<0, write1(f, "(",xx,")"), write1(f, xx)); write1(f, "^5+"); if(yy<0, write1(f, "(",yy,")"), write1(f, yy)); write1(f, "^5+"); if(z<0, write1(f, "(",z,")"), write1(f, z)); write1(f, "^5"); write(f,); )); } ``` ``` \\ This is my PARI/GP program code for WONplate 230 by PDG [May 23, 2024] → so5p.gp \\ Instead of random picks this time all combinations from -b up to b are scanned, \\ for one particular value n. \\ But this comes with a price namely it runs for a very long time... f="D:/Teksten2024/Vijfdemachten666.txt"; { n=666 ; b=50; print("\e[38;5;92m",n," z<=",b,"\e[38;5;37m");print; write(f, n" z<="b);write(f,); for(y=-b,b, for(x=-b,b, for(w=-b,b, for(v=-b,b, fif=n-v^5-w^5-x^5-y^5; fiff=sqrtn(abs(fif),5); z=floor(fiff*sign(fif)); if(fiff==floor(fiff), \\ if(fiff==floor(fiff)&&v+w<>0&&v+x<>0&&v+y<>0&&v+z<>0&&w+x<>0&&w+y<>0&&w+z<>0&&x+y<>0&&x+z<>0&&y+z<>0, \\[ COPY THE BLUE SORTING/OUTPUT CODE FROM ABOVE HERE ] ))))); } print(Strchr(13)); ```
 A000230 Prime Curios! Prime Puzzle Wikipedia 230 Le nombre 230
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