
theorem
  9319 is prime
proof
  now
    9319 = 2*4659 + 1; hence not 2 divides 9319 by NAT_4:9;
    9319 = 3*3106 + 1; hence not 3 divides 9319 by NAT_4:9;
    9319 = 5*1863 + 4; hence not 5 divides 9319 by NAT_4:9;
    9319 = 7*1331 + 2; hence not 7 divides 9319 by NAT_4:9;
    9319 = 11*847 + 2; hence not 11 divides 9319 by NAT_4:9;
    9319 = 13*716 + 11; hence not 13 divides 9319 by NAT_4:9;
    9319 = 17*548 + 3; hence not 17 divides 9319 by NAT_4:9;
    9319 = 19*490 + 9; hence not 19 divides 9319 by NAT_4:9;
    9319 = 23*405 + 4; hence not 23 divides 9319 by NAT_4:9;
    9319 = 29*321 + 10; hence not 29 divides 9319 by NAT_4:9;
    9319 = 31*300 + 19; hence not 31 divides 9319 by NAT_4:9;
    9319 = 37*251 + 32; hence not 37 divides 9319 by NAT_4:9;
    9319 = 41*227 + 12; hence not 41 divides 9319 by NAT_4:9;
    9319 = 43*216 + 31; hence not 43 divides 9319 by NAT_4:9;
    9319 = 47*198 + 13; hence not 47 divides 9319 by NAT_4:9;
    9319 = 53*175 + 44; hence not 53 divides 9319 by NAT_4:9;
    9319 = 59*157 + 56; hence not 59 divides 9319 by NAT_4:9;
    9319 = 61*152 + 47; hence not 61 divides 9319 by NAT_4:9;
    9319 = 67*139 + 6; hence not 67 divides 9319 by NAT_4:9;
    9319 = 71*131 + 18; hence not 71 divides 9319 by NAT_4:9;
    9319 = 73*127 + 48; hence not 73 divides 9319 by NAT_4:9;
    9319 = 79*117 + 76; hence not 79 divides 9319 by NAT_4:9;
    9319 = 83*112 + 23; hence not 83 divides 9319 by NAT_4:9;
    9319 = 89*104 + 63; hence not 89 divides 9319 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9319 & n is prime
  holds not n divides 9319 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
