
theorem
  2719 is prime
proof
  now
    2719 = 2*1359 + 1; hence not 2 divides 2719 by NAT_4:9;
    2719 = 3*906 + 1; hence not 3 divides 2719 by NAT_4:9;
    2719 = 5*543 + 4; hence not 5 divides 2719 by NAT_4:9;
    2719 = 7*388 + 3; hence not 7 divides 2719 by NAT_4:9;
    2719 = 11*247 + 2; hence not 11 divides 2719 by NAT_4:9;
    2719 = 13*209 + 2; hence not 13 divides 2719 by NAT_4:9;
    2719 = 17*159 + 16; hence not 17 divides 2719 by NAT_4:9;
    2719 = 19*143 + 2; hence not 19 divides 2719 by NAT_4:9;
    2719 = 23*118 + 5; hence not 23 divides 2719 by NAT_4:9;
    2719 = 29*93 + 22; hence not 29 divides 2719 by NAT_4:9;
    2719 = 31*87 + 22; hence not 31 divides 2719 by NAT_4:9;
    2719 = 37*73 + 18; hence not 37 divides 2719 by NAT_4:9;
    2719 = 41*66 + 13; hence not 41 divides 2719 by NAT_4:9;
    2719 = 43*63 + 10; hence not 43 divides 2719 by NAT_4:9;
    2719 = 47*57 + 40; hence not 47 divides 2719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2719 & n is prime
  holds not n divides 2719 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
