
theorem
  719 is prime
proof
  now
    719 = 2*359 + 1; hence not 2 divides 719 by NAT_4:9;
    719 = 3*239 + 2; hence not 3 divides 719 by NAT_4:9;
    719 = 5*143 + 4; hence not 5 divides 719 by NAT_4:9;
    719 = 7*102 + 5; hence not 7 divides 719 by NAT_4:9;
    719 = 11*65 + 4; hence not 11 divides 719 by NAT_4:9;
    719 = 13*55 + 4; hence not 13 divides 719 by NAT_4:9;
    719 = 17*42 + 5; hence not 17 divides 719 by NAT_4:9;
    719 = 19*37 + 16; hence not 19 divides 719 by NAT_4:9;
    719 = 23*31 + 6; hence not 23 divides 719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 719 & n is prime
  holds not n divides 719 by XPRIMET1:18;
  hence thesis by NAT_4:14;
