
theorem
  2111 is prime
proof
  now
    2111 = 2*1055 + 1; hence not 2 divides 2111 by NAT_4:9;
    2111 = 3*703 + 2; hence not 3 divides 2111 by NAT_4:9;
    2111 = 5*422 + 1; hence not 5 divides 2111 by NAT_4:9;
    2111 = 7*301 + 4; hence not 7 divides 2111 by NAT_4:9;
    2111 = 11*191 + 10; hence not 11 divides 2111 by NAT_4:9;
    2111 = 13*162 + 5; hence not 13 divides 2111 by NAT_4:9;
    2111 = 17*124 + 3; hence not 17 divides 2111 by NAT_4:9;
    2111 = 19*111 + 2; hence not 19 divides 2111 by NAT_4:9;
    2111 = 23*91 + 18; hence not 23 divides 2111 by NAT_4:9;
    2111 = 29*72 + 23; hence not 29 divides 2111 by NAT_4:9;
    2111 = 31*68 + 3; hence not 31 divides 2111 by NAT_4:9;
    2111 = 37*57 + 2; hence not 37 divides 2111 by NAT_4:9;
    2111 = 41*51 + 20; hence not 41 divides 2111 by NAT_4:9;
    2111 = 43*49 + 4; hence not 43 divides 2111 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2111 & n is prime
  holds not n divides 2111 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
