
theorem
  9241 is prime
proof
  now
    9241 = 2*4620 + 1; hence not 2 divides 9241 by NAT_4:9;
    9241 = 3*3080 + 1; hence not 3 divides 9241 by NAT_4:9;
    9241 = 5*1848 + 1; hence not 5 divides 9241 by NAT_4:9;
    9241 = 7*1320 + 1; hence not 7 divides 9241 by NAT_4:9;
    9241 = 11*840 + 1; hence not 11 divides 9241 by NAT_4:9;
    9241 = 13*710 + 11; hence not 13 divides 9241 by NAT_4:9;
    9241 = 17*543 + 10; hence not 17 divides 9241 by NAT_4:9;
    9241 = 19*486 + 7; hence not 19 divides 9241 by NAT_4:9;
    9241 = 23*401 + 18; hence not 23 divides 9241 by NAT_4:9;
    9241 = 29*318 + 19; hence not 29 divides 9241 by NAT_4:9;
    9241 = 31*298 + 3; hence not 31 divides 9241 by NAT_4:9;
    9241 = 37*249 + 28; hence not 37 divides 9241 by NAT_4:9;
    9241 = 41*225 + 16; hence not 41 divides 9241 by NAT_4:9;
    9241 = 43*214 + 39; hence not 43 divides 9241 by NAT_4:9;
    9241 = 47*196 + 29; hence not 47 divides 9241 by NAT_4:9;
    9241 = 53*174 + 19; hence not 53 divides 9241 by NAT_4:9;
    9241 = 59*156 + 37; hence not 59 divides 9241 by NAT_4:9;
    9241 = 61*151 + 30; hence not 61 divides 9241 by NAT_4:9;
    9241 = 67*137 + 62; hence not 67 divides 9241 by NAT_4:9;
    9241 = 71*130 + 11; hence not 71 divides 9241 by NAT_4:9;
    9241 = 73*126 + 43; hence not 73 divides 9241 by NAT_4:9;
    9241 = 79*116 + 77; hence not 79 divides 9241 by NAT_4:9;
    9241 = 83*111 + 28; hence not 83 divides 9241 by NAT_4:9;
    9241 = 89*103 + 74; hence not 89 divides 9241 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9241 & n is prime
  holds not n divides 9241 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
