
theorem
  9721 is prime
proof
  now
    9721 = 2*4860 + 1; hence not 2 divides 9721 by NAT_4:9;
    9721 = 3*3240 + 1; hence not 3 divides 9721 by NAT_4:9;
    9721 = 5*1944 + 1; hence not 5 divides 9721 by NAT_4:9;
    9721 = 7*1388 + 5; hence not 7 divides 9721 by NAT_4:9;
    9721 = 11*883 + 8; hence not 11 divides 9721 by NAT_4:9;
    9721 = 13*747 + 10; hence not 13 divides 9721 by NAT_4:9;
    9721 = 17*571 + 14; hence not 17 divides 9721 by NAT_4:9;
    9721 = 19*511 + 12; hence not 19 divides 9721 by NAT_4:9;
    9721 = 23*422 + 15; hence not 23 divides 9721 by NAT_4:9;
    9721 = 29*335 + 6; hence not 29 divides 9721 by NAT_4:9;
    9721 = 31*313 + 18; hence not 31 divides 9721 by NAT_4:9;
    9721 = 37*262 + 27; hence not 37 divides 9721 by NAT_4:9;
    9721 = 41*237 + 4; hence not 41 divides 9721 by NAT_4:9;
    9721 = 43*226 + 3; hence not 43 divides 9721 by NAT_4:9;
    9721 = 47*206 + 39; hence not 47 divides 9721 by NAT_4:9;
    9721 = 53*183 + 22; hence not 53 divides 9721 by NAT_4:9;
    9721 = 59*164 + 45; hence not 59 divides 9721 by NAT_4:9;
    9721 = 61*159 + 22; hence not 61 divides 9721 by NAT_4:9;
    9721 = 67*145 + 6; hence not 67 divides 9721 by NAT_4:9;
    9721 = 71*136 + 65; hence not 71 divides 9721 by NAT_4:9;
    9721 = 73*133 + 12; hence not 73 divides 9721 by NAT_4:9;
    9721 = 79*123 + 4; hence not 79 divides 9721 by NAT_4:9;
    9721 = 83*117 + 10; hence not 83 divides 9721 by NAT_4:9;
    9721 = 89*109 + 20; hence not 89 divides 9721 by NAT_4:9;
    9721 = 97*100 + 21; hence not 97 divides 9721 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9721 & n is prime
  holds not n divides 9721 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
