
theorem
  9173 is prime
proof
  now
    9173 = 2*4586 + 1; hence not 2 divides 9173 by NAT_4:9;
    9173 = 3*3057 + 2; hence not 3 divides 9173 by NAT_4:9;
    9173 = 5*1834 + 3; hence not 5 divides 9173 by NAT_4:9;
    9173 = 7*1310 + 3; hence not 7 divides 9173 by NAT_4:9;
    9173 = 11*833 + 10; hence not 11 divides 9173 by NAT_4:9;
    9173 = 13*705 + 8; hence not 13 divides 9173 by NAT_4:9;
    9173 = 17*539 + 10; hence not 17 divides 9173 by NAT_4:9;
    9173 = 19*482 + 15; hence not 19 divides 9173 by NAT_4:9;
    9173 = 23*398 + 19; hence not 23 divides 9173 by NAT_4:9;
    9173 = 29*316 + 9; hence not 29 divides 9173 by NAT_4:9;
    9173 = 31*295 + 28; hence not 31 divides 9173 by NAT_4:9;
    9173 = 37*247 + 34; hence not 37 divides 9173 by NAT_4:9;
    9173 = 41*223 + 30; hence not 41 divides 9173 by NAT_4:9;
    9173 = 43*213 + 14; hence not 43 divides 9173 by NAT_4:9;
    9173 = 47*195 + 8; hence not 47 divides 9173 by NAT_4:9;
    9173 = 53*173 + 4; hence not 53 divides 9173 by NAT_4:9;
    9173 = 59*155 + 28; hence not 59 divides 9173 by NAT_4:9;
    9173 = 61*150 + 23; hence not 61 divides 9173 by NAT_4:9;
    9173 = 67*136 + 61; hence not 67 divides 9173 by NAT_4:9;
    9173 = 71*129 + 14; hence not 71 divides 9173 by NAT_4:9;
    9173 = 73*125 + 48; hence not 73 divides 9173 by NAT_4:9;
    9173 = 79*116 + 9; hence not 79 divides 9173 by NAT_4:9;
    9173 = 83*110 + 43; hence not 83 divides 9173 by NAT_4:9;
    9173 = 89*103 + 6; hence not 89 divides 9173 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9173 & n is prime
  holds not n divides 9173 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
