
theorem
  2213 is prime
proof
  now
    2213 = 2*1106 + 1; hence not 2 divides 2213 by NAT_4:9;
    2213 = 3*737 + 2; hence not 3 divides 2213 by NAT_4:9;
    2213 = 5*442 + 3; hence not 5 divides 2213 by NAT_4:9;
    2213 = 7*316 + 1; hence not 7 divides 2213 by NAT_4:9;
    2213 = 11*201 + 2; hence not 11 divides 2213 by NAT_4:9;
    2213 = 13*170 + 3; hence not 13 divides 2213 by NAT_4:9;
    2213 = 17*130 + 3; hence not 17 divides 2213 by NAT_4:9;
    2213 = 19*116 + 9; hence not 19 divides 2213 by NAT_4:9;
    2213 = 23*96 + 5; hence not 23 divides 2213 by NAT_4:9;
    2213 = 29*76 + 9; hence not 29 divides 2213 by NAT_4:9;
    2213 = 31*71 + 12; hence not 31 divides 2213 by NAT_4:9;
    2213 = 37*59 + 30; hence not 37 divides 2213 by NAT_4:9;
    2213 = 41*53 + 40; hence not 41 divides 2213 by NAT_4:9;
    2213 = 43*51 + 20; hence not 43 divides 2213 by NAT_4:9;
    2213 = 47*47 + 4; hence not 47 divides 2213 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2213 & n is prime
  holds not n divides 2213 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
