
theorem
  6703 is prime
proof
  now
    6703 = 2*3351 + 1; hence not 2 divides 6703 by NAT_4:9;
    6703 = 3*2234 + 1; hence not 3 divides 6703 by NAT_4:9;
    6703 = 5*1340 + 3; hence not 5 divides 6703 by NAT_4:9;
    6703 = 7*957 + 4; hence not 7 divides 6703 by NAT_4:9;
    6703 = 11*609 + 4; hence not 11 divides 6703 by NAT_4:9;
    6703 = 13*515 + 8; hence not 13 divides 6703 by NAT_4:9;
    6703 = 17*394 + 5; hence not 17 divides 6703 by NAT_4:9;
    6703 = 19*352 + 15; hence not 19 divides 6703 by NAT_4:9;
    6703 = 23*291 + 10; hence not 23 divides 6703 by NAT_4:9;
    6703 = 29*231 + 4; hence not 29 divides 6703 by NAT_4:9;
    6703 = 31*216 + 7; hence not 31 divides 6703 by NAT_4:9;
    6703 = 37*181 + 6; hence not 37 divides 6703 by NAT_4:9;
    6703 = 41*163 + 20; hence not 41 divides 6703 by NAT_4:9;
    6703 = 43*155 + 38; hence not 43 divides 6703 by NAT_4:9;
    6703 = 47*142 + 29; hence not 47 divides 6703 by NAT_4:9;
    6703 = 53*126 + 25; hence not 53 divides 6703 by NAT_4:9;
    6703 = 59*113 + 36; hence not 59 divides 6703 by NAT_4:9;
    6703 = 61*109 + 54; hence not 61 divides 6703 by NAT_4:9;
    6703 = 67*100 + 3; hence not 67 divides 6703 by NAT_4:9;
    6703 = 71*94 + 29; hence not 71 divides 6703 by NAT_4:9;
    6703 = 73*91 + 60; hence not 73 divides 6703 by NAT_4:9;
    6703 = 79*84 + 67; hence not 79 divides 6703 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6703 & n is prime
  holds not n divides 6703 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
