
theorem
  2543 is prime
proof
  now
    2543 = 2*1271 + 1; hence not 2 divides 2543 by NAT_4:9;
    2543 = 3*847 + 2; hence not 3 divides 2543 by NAT_4:9;
    2543 = 5*508 + 3; hence not 5 divides 2543 by NAT_4:9;
    2543 = 7*363 + 2; hence not 7 divides 2543 by NAT_4:9;
    2543 = 11*231 + 2; hence not 11 divides 2543 by NAT_4:9;
    2543 = 13*195 + 8; hence not 13 divides 2543 by NAT_4:9;
    2543 = 17*149 + 10; hence not 17 divides 2543 by NAT_4:9;
    2543 = 19*133 + 16; hence not 19 divides 2543 by NAT_4:9;
    2543 = 23*110 + 13; hence not 23 divides 2543 by NAT_4:9;
    2543 = 29*87 + 20; hence not 29 divides 2543 by NAT_4:9;
    2543 = 31*82 + 1; hence not 31 divides 2543 by NAT_4:9;
    2543 = 37*68 + 27; hence not 37 divides 2543 by NAT_4:9;
    2543 = 41*62 + 1; hence not 41 divides 2543 by NAT_4:9;
    2543 = 43*59 + 6; hence not 43 divides 2543 by NAT_4:9;
    2543 = 47*54 + 5; hence not 47 divides 2543 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2543 & n is prime
  holds not n divides 2543 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
