
theorem
  9803 is prime
proof
  now
    9803 = 2*4901 + 1; hence not 2 divides 9803 by NAT_4:9;
    9803 = 3*3267 + 2; hence not 3 divides 9803 by NAT_4:9;
    9803 = 5*1960 + 3; hence not 5 divides 9803 by NAT_4:9;
    9803 = 7*1400 + 3; hence not 7 divides 9803 by NAT_4:9;
    9803 = 11*891 + 2; hence not 11 divides 9803 by NAT_4:9;
    9803 = 13*754 + 1; hence not 13 divides 9803 by NAT_4:9;
    9803 = 17*576 + 11; hence not 17 divides 9803 by NAT_4:9;
    9803 = 19*515 + 18; hence not 19 divides 9803 by NAT_4:9;
    9803 = 23*426 + 5; hence not 23 divides 9803 by NAT_4:9;
    9803 = 29*338 + 1; hence not 29 divides 9803 by NAT_4:9;
    9803 = 31*316 + 7; hence not 31 divides 9803 by NAT_4:9;
    9803 = 37*264 + 35; hence not 37 divides 9803 by NAT_4:9;
    9803 = 41*239 + 4; hence not 41 divides 9803 by NAT_4:9;
    9803 = 43*227 + 42; hence not 43 divides 9803 by NAT_4:9;
    9803 = 47*208 + 27; hence not 47 divides 9803 by NAT_4:9;
    9803 = 53*184 + 51; hence not 53 divides 9803 by NAT_4:9;
    9803 = 59*166 + 9; hence not 59 divides 9803 by NAT_4:9;
    9803 = 61*160 + 43; hence not 61 divides 9803 by NAT_4:9;
    9803 = 67*146 + 21; hence not 67 divides 9803 by NAT_4:9;
    9803 = 71*138 + 5; hence not 71 divides 9803 by NAT_4:9;
    9803 = 73*134 + 21; hence not 73 divides 9803 by NAT_4:9;
    9803 = 79*124 + 7; hence not 79 divides 9803 by NAT_4:9;
    9803 = 83*118 + 9; hence not 83 divides 9803 by NAT_4:9;
    9803 = 89*110 + 13; hence not 89 divides 9803 by NAT_4:9;
    9803 = 97*101 + 6; hence not 97 divides 9803 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9803 & n is prime
  holds not n divides 9803 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
