
theorem
  727 is prime
proof
  now
    727 = 2*363 + 1; hence not 2 divides 727 by NAT_4:9;
    727 = 3*242 + 1; hence not 3 divides 727 by NAT_4:9;
    727 = 5*145 + 2; hence not 5 divides 727 by NAT_4:9;
    727 = 7*103 + 6; hence not 7 divides 727 by NAT_4:9;
    727 = 11*66 + 1; hence not 11 divides 727 by NAT_4:9;
    727 = 13*55 + 12; hence not 13 divides 727 by NAT_4:9;
    727 = 17*42 + 13; hence not 17 divides 727 by NAT_4:9;
    727 = 19*38 + 5; hence not 19 divides 727 by NAT_4:9;
    727 = 23*31 + 14; hence not 23 divides 727 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 727 & n is prime
  holds not n divides 727 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
