
theorem
  6719 is prime
proof
  now
    6719 = 2*3359 + 1; hence not 2 divides 6719 by NAT_4:9;
    6719 = 3*2239 + 2; hence not 3 divides 6719 by NAT_4:9;
    6719 = 5*1343 + 4; hence not 5 divides 6719 by NAT_4:9;
    6719 = 7*959 + 6; hence not 7 divides 6719 by NAT_4:9;
    6719 = 11*610 + 9; hence not 11 divides 6719 by NAT_4:9;
    6719 = 13*516 + 11; hence not 13 divides 6719 by NAT_4:9;
    6719 = 17*395 + 4; hence not 17 divides 6719 by NAT_4:9;
    6719 = 19*353 + 12; hence not 19 divides 6719 by NAT_4:9;
    6719 = 23*292 + 3; hence not 23 divides 6719 by NAT_4:9;
    6719 = 29*231 + 20; hence not 29 divides 6719 by NAT_4:9;
    6719 = 31*216 + 23; hence not 31 divides 6719 by NAT_4:9;
    6719 = 37*181 + 22; hence not 37 divides 6719 by NAT_4:9;
    6719 = 41*163 + 36; hence not 41 divides 6719 by NAT_4:9;
    6719 = 43*156 + 11; hence not 43 divides 6719 by NAT_4:9;
    6719 = 47*142 + 45; hence not 47 divides 6719 by NAT_4:9;
    6719 = 53*126 + 41; hence not 53 divides 6719 by NAT_4:9;
    6719 = 59*113 + 52; hence not 59 divides 6719 by NAT_4:9;
    6719 = 61*110 + 9; hence not 61 divides 6719 by NAT_4:9;
    6719 = 67*100 + 19; hence not 67 divides 6719 by NAT_4:9;
    6719 = 71*94 + 45; hence not 71 divides 6719 by NAT_4:9;
    6719 = 73*92 + 3; hence not 73 divides 6719 by NAT_4:9;
    6719 = 79*85 + 4; hence not 79 divides 6719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6719 & n is prime
  holds not n divides 6719 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
