
theorem
  1123 is prime
proof
  now
    1123 = 2*561 + 1; hence not 2 divides 1123 by NAT_4:9;
    1123 = 3*374 + 1; hence not 3 divides 1123 by NAT_4:9;
    1123 = 5*224 + 3; hence not 5 divides 1123 by NAT_4:9;
    1123 = 7*160 + 3; hence not 7 divides 1123 by NAT_4:9;
    1123 = 11*102 + 1; hence not 11 divides 1123 by NAT_4:9;
    1123 = 13*86 + 5; hence not 13 divides 1123 by NAT_4:9;
    1123 = 17*66 + 1; hence not 17 divides 1123 by NAT_4:9;
    1123 = 19*59 + 2; hence not 19 divides 1123 by NAT_4:9;
    1123 = 23*48 + 19; hence not 23 divides 1123 by NAT_4:9;
    1123 = 29*38 + 21; hence not 29 divides 1123 by NAT_4:9;
    1123 = 31*36 + 7; hence not 31 divides 1123 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1123 & n is prime
  holds not n divides 1123 by XPRIMET1:22;
  hence thesis by NAT_4:14;
