
theorem
  9349 is prime
proof
  now
    9349 = 2*4674 + 1; hence not 2 divides 9349 by NAT_4:9;
    9349 = 3*3116 + 1; hence not 3 divides 9349 by NAT_4:9;
    9349 = 5*1869 + 4; hence not 5 divides 9349 by NAT_4:9;
    9349 = 7*1335 + 4; hence not 7 divides 9349 by NAT_4:9;
    9349 = 11*849 + 10; hence not 11 divides 9349 by NAT_4:9;
    9349 = 13*719 + 2; hence not 13 divides 9349 by NAT_4:9;
    9349 = 17*549 + 16; hence not 17 divides 9349 by NAT_4:9;
    9349 = 19*492 + 1; hence not 19 divides 9349 by NAT_4:9;
    9349 = 23*406 + 11; hence not 23 divides 9349 by NAT_4:9;
    9349 = 29*322 + 11; hence not 29 divides 9349 by NAT_4:9;
    9349 = 31*301 + 18; hence not 31 divides 9349 by NAT_4:9;
    9349 = 37*252 + 25; hence not 37 divides 9349 by NAT_4:9;
    9349 = 41*228 + 1; hence not 41 divides 9349 by NAT_4:9;
    9349 = 43*217 + 18; hence not 43 divides 9349 by NAT_4:9;
    9349 = 47*198 + 43; hence not 47 divides 9349 by NAT_4:9;
    9349 = 53*176 + 21; hence not 53 divides 9349 by NAT_4:9;
    9349 = 59*158 + 27; hence not 59 divides 9349 by NAT_4:9;
    9349 = 61*153 + 16; hence not 61 divides 9349 by NAT_4:9;
    9349 = 67*139 + 36; hence not 67 divides 9349 by NAT_4:9;
    9349 = 71*131 + 48; hence not 71 divides 9349 by NAT_4:9;
    9349 = 73*128 + 5; hence not 73 divides 9349 by NAT_4:9;
    9349 = 79*118 + 27; hence not 79 divides 9349 by NAT_4:9;
    9349 = 83*112 + 53; hence not 83 divides 9349 by NAT_4:9;
    9349 = 89*105 + 4; hence not 89 divides 9349 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9349 & n is prime
  holds not n divides 9349 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
