
theorem
  2203 is prime
proof
  now
    2203 = 2*1101 + 1; hence not 2 divides 2203 by NAT_4:9;
    2203 = 3*734 + 1; hence not 3 divides 2203 by NAT_4:9;
    2203 = 5*440 + 3; hence not 5 divides 2203 by NAT_4:9;
    2203 = 7*314 + 5; hence not 7 divides 2203 by NAT_4:9;
    2203 = 11*200 + 3; hence not 11 divides 2203 by NAT_4:9;
    2203 = 13*169 + 6; hence not 13 divides 2203 by NAT_4:9;
    2203 = 17*129 + 10; hence not 17 divides 2203 by NAT_4:9;
    2203 = 19*115 + 18; hence not 19 divides 2203 by NAT_4:9;
    2203 = 23*95 + 18; hence not 23 divides 2203 by NAT_4:9;
    2203 = 29*75 + 28; hence not 29 divides 2203 by NAT_4:9;
    2203 = 31*71 + 2; hence not 31 divides 2203 by NAT_4:9;
    2203 = 37*59 + 20; hence not 37 divides 2203 by NAT_4:9;
    2203 = 41*53 + 30; hence not 41 divides 2203 by NAT_4:9;
    2203 = 43*51 + 10; hence not 43 divides 2203 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2203 & n is prime
  holds not n divides 2203 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
