
theorem
  9239 is prime
proof
  now
    9239 = 2*4619 + 1; hence not 2 divides 9239 by NAT_4:9;
    9239 = 3*3079 + 2; hence not 3 divides 9239 by NAT_4:9;
    9239 = 5*1847 + 4; hence not 5 divides 9239 by NAT_4:9;
    9239 = 7*1319 + 6; hence not 7 divides 9239 by NAT_4:9;
    9239 = 11*839 + 10; hence not 11 divides 9239 by NAT_4:9;
    9239 = 13*710 + 9; hence not 13 divides 9239 by NAT_4:9;
    9239 = 17*543 + 8; hence not 17 divides 9239 by NAT_4:9;
    9239 = 19*486 + 5; hence not 19 divides 9239 by NAT_4:9;
    9239 = 23*401 + 16; hence not 23 divides 9239 by NAT_4:9;
    9239 = 29*318 + 17; hence not 29 divides 9239 by NAT_4:9;
    9239 = 31*298 + 1; hence not 31 divides 9239 by NAT_4:9;
    9239 = 37*249 + 26; hence not 37 divides 9239 by NAT_4:9;
    9239 = 41*225 + 14; hence not 41 divides 9239 by NAT_4:9;
    9239 = 43*214 + 37; hence not 43 divides 9239 by NAT_4:9;
    9239 = 47*196 + 27; hence not 47 divides 9239 by NAT_4:9;
    9239 = 53*174 + 17; hence not 53 divides 9239 by NAT_4:9;
    9239 = 59*156 + 35; hence not 59 divides 9239 by NAT_4:9;
    9239 = 61*151 + 28; hence not 61 divides 9239 by NAT_4:9;
    9239 = 67*137 + 60; hence not 67 divides 9239 by NAT_4:9;
    9239 = 71*130 + 9; hence not 71 divides 9239 by NAT_4:9;
    9239 = 73*126 + 41; hence not 73 divides 9239 by NAT_4:9;
    9239 = 79*116 + 75; hence not 79 divides 9239 by NAT_4:9;
    9239 = 83*111 + 26; hence not 83 divides 9239 by NAT_4:9;
    9239 = 89*103 + 72; hence not 89 divides 9239 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9239 & n is prime
  holds not n divides 9239 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
