
theorem
  2243 is prime
proof
  now
    2243 = 2*1121 + 1; hence not 2 divides 2243 by NAT_4:9;
    2243 = 3*747 + 2; hence not 3 divides 2243 by NAT_4:9;
    2243 = 5*448 + 3; hence not 5 divides 2243 by NAT_4:9;
    2243 = 7*320 + 3; hence not 7 divides 2243 by NAT_4:9;
    2243 = 11*203 + 10; hence not 11 divides 2243 by NAT_4:9;
    2243 = 13*172 + 7; hence not 13 divides 2243 by NAT_4:9;
    2243 = 17*131 + 16; hence not 17 divides 2243 by NAT_4:9;
    2243 = 19*118 + 1; hence not 19 divides 2243 by NAT_4:9;
    2243 = 23*97 + 12; hence not 23 divides 2243 by NAT_4:9;
    2243 = 29*77 + 10; hence not 29 divides 2243 by NAT_4:9;
    2243 = 31*72 + 11; hence not 31 divides 2243 by NAT_4:9;
    2243 = 37*60 + 23; hence not 37 divides 2243 by NAT_4:9;
    2243 = 41*54 + 29; hence not 41 divides 2243 by NAT_4:9;
    2243 = 43*52 + 7; hence not 43 divides 2243 by NAT_4:9;
    2243 = 47*47 + 34; hence not 47 divides 2243 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2243 & n is prime
  holds not n divides 2243 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
