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 2021-07-30, 17:55 #14 Alberico Lepore     May 2017 ITALY 10000010102 Posts Code: i=0 while(i<10) { solve this system and memorize y(i) and r(i) sqrt(N/((10+i)/10))=a , ((10+i)/10*a+a-4)/8=x , 2*x*(x+1)-y*(y-1)/2=(N-3)/8 , (sqrt(32*x+1)+1)/2=b , [b*(b-1)/2-(sqrt(32*(x-b)+1)+1)/2*[(sqrt(32*(x-b)+1)+1)/2-1]/2]/2=r } j=0 while (!(N mod p ==0 && p!=1 && p!=N)){ i=0 while(i<10) { solve this system with unique integer solution of h 2*(h)*(h-1)<(N-3)/8+k*(k-1)/2<=2*(h)*(h+1) , 2*(x)*(x+1)-y*(y-1)/2=(N-3)/8 , x-(sqrt(32*x+1)+1)/2[range of x]>=1 if exist (*) if exist { choose the only possible integer solution of x x-(sqrt(32*x+1)+1)/2=h 2*(x)*(x+1)-y*(y-1)/2=(N-3)/8 calculate p p=4*x+1-2*(y-1) } i++ } j++ } Example N=390644893234047643 , sqrt(N/(15/10))=a , (15/10*a+a-4)/8=x , 2*x*(x+1)-y*(y-1)/2=(N-3)/8 , (sqrt(32*x+1)+1)/2=b , [b*(b-1)/2-(sqrt(32*(x-b)+1)+1)/2*[(sqrt(32*(x-b)+1)+1)/2-1]/2]/2=r r=71437,..... N=390644893234047643 , 2*(h)*(h-1)<(N-3)/8+k*(k-1)/2<=2*(h)*(h+1) , 2*(x)*(x+1)-y*(y-1)/2=(N-3)/8 , x-(sqrt(32*x+1)+1)/2= 1 & <2