
theorem
  1103 is prime
proof
  now
    1103 = 2*551 + 1; hence not 2 divides 1103 by NAT_4:9;
    1103 = 3*367 + 2; hence not 3 divides 1103 by NAT_4:9;
    1103 = 5*220 + 3; hence not 5 divides 1103 by NAT_4:9;
    1103 = 7*157 + 4; hence not 7 divides 1103 by NAT_4:9;
    1103 = 11*100 + 3; hence not 11 divides 1103 by NAT_4:9;
    1103 = 13*84 + 11; hence not 13 divides 1103 by NAT_4:9;
    1103 = 17*64 + 15; hence not 17 divides 1103 by NAT_4:9;
    1103 = 19*58 + 1; hence not 19 divides 1103 by NAT_4:9;
    1103 = 23*47 + 22; hence not 23 divides 1103 by NAT_4:9;
    1103 = 29*38 + 1; hence not 29 divides 1103 by NAT_4:9;
    1103 = 31*35 + 18; hence not 31 divides 1103 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1103 & n is prime
  holds not n divides 1103 by XPRIMET1:22;
  hence thesis by NAT_4:14;
