
theorem
  9323 is prime
proof
  now
    9323 = 2*4661 + 1; hence not 2 divides 9323 by NAT_4:9;
    9323 = 3*3107 + 2; hence not 3 divides 9323 by NAT_4:9;
    9323 = 5*1864 + 3; hence not 5 divides 9323 by NAT_4:9;
    9323 = 7*1331 + 6; hence not 7 divides 9323 by NAT_4:9;
    9323 = 11*847 + 6; hence not 11 divides 9323 by NAT_4:9;
    9323 = 13*717 + 2; hence not 13 divides 9323 by NAT_4:9;
    9323 = 17*548 + 7; hence not 17 divides 9323 by NAT_4:9;
    9323 = 19*490 + 13; hence not 19 divides 9323 by NAT_4:9;
    9323 = 23*405 + 8; hence not 23 divides 9323 by NAT_4:9;
    9323 = 29*321 + 14; hence not 29 divides 9323 by NAT_4:9;
    9323 = 31*300 + 23; hence not 31 divides 9323 by NAT_4:9;
    9323 = 37*251 + 36; hence not 37 divides 9323 by NAT_4:9;
    9323 = 41*227 + 16; hence not 41 divides 9323 by NAT_4:9;
    9323 = 43*216 + 35; hence not 43 divides 9323 by NAT_4:9;
    9323 = 47*198 + 17; hence not 47 divides 9323 by NAT_4:9;
    9323 = 53*175 + 48; hence not 53 divides 9323 by NAT_4:9;
    9323 = 59*158 + 1; hence not 59 divides 9323 by NAT_4:9;
    9323 = 61*152 + 51; hence not 61 divides 9323 by NAT_4:9;
    9323 = 67*139 + 10; hence not 67 divides 9323 by NAT_4:9;
    9323 = 71*131 + 22; hence not 71 divides 9323 by NAT_4:9;
    9323 = 73*127 + 52; hence not 73 divides 9323 by NAT_4:9;
    9323 = 79*118 + 1; hence not 79 divides 9323 by NAT_4:9;
    9323 = 83*112 + 27; hence not 83 divides 9323 by NAT_4:9;
    9323 = 89*104 + 67; hence not 89 divides 9323 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9323 & n is prime
  holds not n divides 9323 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
