6300846559 is such that 6 is divisible by 2; 63, by 3; 630, by 5; 6300, by 7; and, in general, if you take its first N digits, it will be divisible by the N-th prime.

There is only one other such 10 digit number: can you find it?

The following gawk script runs in 0.04 seconds in my Linux machine, and produces 0000000000, 6300846559, and 8757193191

BEGIN {


  for (a=0; a<10; a++) if (check(a,2)) {


    for (b=0; b<10; b++) if (check(a b,3)) {


      for (c=0; c<10; c++) if (check(a b c,5)) {


        for (d=0; d<10; d++) if (check(a b c d,7)) {


          for (e=0; e<10; e++) if (check(a b c d e,11)) {


            for (f=0; f<10; f++) if (check(a b c d e f,13)) {


              for (g=0; g<10; g++) if (check(a b c d e f g,17)) {


                for (h=0; h<10; h++) if (check(a b c d e f g h,19)) {


                  for (i=0; i<10; i++) if (check(a b c d e f g h i,23)) {


                    for (j=0; j<10; j++) if (check(a b c d e f g h i j,29)) {


                      print a b c d e f g h i j;


                    }


                  }


                }


              }


            }


          }


        }


      }


    }


  }


}





function check(nnn,pp) {


  nnn += 0


  return ((nnn % pp) == 0);


}
Edited on January 4, 2005, 5:24 pm		

		

			

			

 			
			

				Posted by Federico Kereki
				on 2005-01-04 17:19:47