
theorem
  1223 is prime
proof
  now
    1223 = 2*611 + 1; hence not 2 divides 1223 by NAT_4:9;
    1223 = 3*407 + 2; hence not 3 divides 1223 by NAT_4:9;
    1223 = 5*244 + 3; hence not 5 divides 1223 by NAT_4:9;
    1223 = 7*174 + 5; hence not 7 divides 1223 by NAT_4:9;
    1223 = 11*111 + 2; hence not 11 divides 1223 by NAT_4:9;
    1223 = 13*94 + 1; hence not 13 divides 1223 by NAT_4:9;
    1223 = 17*71 + 16; hence not 17 divides 1223 by NAT_4:9;
    1223 = 19*64 + 7; hence not 19 divides 1223 by NAT_4:9;
    1223 = 23*53 + 4; hence not 23 divides 1223 by NAT_4:9;
    1223 = 29*42 + 5; hence not 29 divides 1223 by NAT_4:9;
    1223 = 31*39 + 14; hence not 31 divides 1223 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1223 & n is prime
  holds not n divides 1223 by XPRIMET1:22;
  hence thesis by NAT_4:14;
