
theorem
  739 is prime
proof
  now
    739 = 2*369 + 1; hence not 2 divides 739 by NAT_4:9;
    739 = 3*246 + 1; hence not 3 divides 739 by NAT_4:9;
    739 = 5*147 + 4; hence not 5 divides 739 by NAT_4:9;
    739 = 7*105 + 4; hence not 7 divides 739 by NAT_4:9;
    739 = 11*67 + 2; hence not 11 divides 739 by NAT_4:9;
    739 = 13*56 + 11; hence not 13 divides 739 by NAT_4:9;
    739 = 17*43 + 8; hence not 17 divides 739 by NAT_4:9;
    739 = 19*38 + 17; hence not 19 divides 739 by NAT_4:9;
    739 = 23*32 + 3; hence not 23 divides 739 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 739 & n is prime
  holds not n divides 739 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
