
theorem
  8389 is prime
proof
  now
    8389 = 2*4194 + 1; hence not 2 divides 8389 by NAT_4:9;
    8389 = 3*2796 + 1; hence not 3 divides 8389 by NAT_4:9;
    8389 = 5*1677 + 4; hence not 5 divides 8389 by NAT_4:9;
    8389 = 7*1198 + 3; hence not 7 divides 8389 by NAT_4:9;
    8389 = 11*762 + 7; hence not 11 divides 8389 by NAT_4:9;
    8389 = 13*645 + 4; hence not 13 divides 8389 by NAT_4:9;
    8389 = 17*493 + 8; hence not 17 divides 8389 by NAT_4:9;
    8389 = 19*441 + 10; hence not 19 divides 8389 by NAT_4:9;
    8389 = 23*364 + 17; hence not 23 divides 8389 by NAT_4:9;
    8389 = 29*289 + 8; hence not 29 divides 8389 by NAT_4:9;
    8389 = 31*270 + 19; hence not 31 divides 8389 by NAT_4:9;
    8389 = 37*226 + 27; hence not 37 divides 8389 by NAT_4:9;
    8389 = 41*204 + 25; hence not 41 divides 8389 by NAT_4:9;
    8389 = 43*195 + 4; hence not 43 divides 8389 by NAT_4:9;
    8389 = 47*178 + 23; hence not 47 divides 8389 by NAT_4:9;
    8389 = 53*158 + 15; hence not 53 divides 8389 by NAT_4:9;
    8389 = 59*142 + 11; hence not 59 divides 8389 by NAT_4:9;
    8389 = 61*137 + 32; hence not 61 divides 8389 by NAT_4:9;
    8389 = 67*125 + 14; hence not 67 divides 8389 by NAT_4:9;
    8389 = 71*118 + 11; hence not 71 divides 8389 by NAT_4:9;
    8389 = 73*114 + 67; hence not 73 divides 8389 by NAT_4:9;
    8389 = 79*106 + 15; hence not 79 divides 8389 by NAT_4:9;
    8389 = 83*101 + 6; hence not 83 divides 8389 by NAT_4:9;
    8389 = 89*94 + 23; hence not 89 divides 8389 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8389 & n is prime
  holds not n divides 8389 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
