
theorem
  9221 is prime
proof
  now
    9221 = 2*4610 + 1; hence not 2 divides 9221 by NAT_4:9;
    9221 = 3*3073 + 2; hence not 3 divides 9221 by NAT_4:9;
    9221 = 5*1844 + 1; hence not 5 divides 9221 by NAT_4:9;
    9221 = 7*1317 + 2; hence not 7 divides 9221 by NAT_4:9;
    9221 = 11*838 + 3; hence not 11 divides 9221 by NAT_4:9;
    9221 = 13*709 + 4; hence not 13 divides 9221 by NAT_4:9;
    9221 = 17*542 + 7; hence not 17 divides 9221 by NAT_4:9;
    9221 = 19*485 + 6; hence not 19 divides 9221 by NAT_4:9;
    9221 = 23*400 + 21; hence not 23 divides 9221 by NAT_4:9;
    9221 = 29*317 + 28; hence not 29 divides 9221 by NAT_4:9;
    9221 = 31*297 + 14; hence not 31 divides 9221 by NAT_4:9;
    9221 = 37*249 + 8; hence not 37 divides 9221 by NAT_4:9;
    9221 = 41*224 + 37; hence not 41 divides 9221 by NAT_4:9;
    9221 = 43*214 + 19; hence not 43 divides 9221 by NAT_4:9;
    9221 = 47*196 + 9; hence not 47 divides 9221 by NAT_4:9;
    9221 = 53*173 + 52; hence not 53 divides 9221 by NAT_4:9;
    9221 = 59*156 + 17; hence not 59 divides 9221 by NAT_4:9;
    9221 = 61*151 + 10; hence not 61 divides 9221 by NAT_4:9;
    9221 = 67*137 + 42; hence not 67 divides 9221 by NAT_4:9;
    9221 = 71*129 + 62; hence not 71 divides 9221 by NAT_4:9;
    9221 = 73*126 + 23; hence not 73 divides 9221 by NAT_4:9;
    9221 = 79*116 + 57; hence not 79 divides 9221 by NAT_4:9;
    9221 = 83*111 + 8; hence not 83 divides 9221 by NAT_4:9;
    9221 = 89*103 + 54; hence not 89 divides 9221 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9221 & n is prime
  holds not n divides 9221 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
