
theorem
  9343 is prime
proof
  now
    9343 = 2*4671 + 1; hence not 2 divides 9343 by NAT_4:9;
    9343 = 3*3114 + 1; hence not 3 divides 9343 by NAT_4:9;
    9343 = 5*1868 + 3; hence not 5 divides 9343 by NAT_4:9;
    9343 = 7*1334 + 5; hence not 7 divides 9343 by NAT_4:9;
    9343 = 11*849 + 4; hence not 11 divides 9343 by NAT_4:9;
    9343 = 13*718 + 9; hence not 13 divides 9343 by NAT_4:9;
    9343 = 17*549 + 10; hence not 17 divides 9343 by NAT_4:9;
    9343 = 19*491 + 14; hence not 19 divides 9343 by NAT_4:9;
    9343 = 23*406 + 5; hence not 23 divides 9343 by NAT_4:9;
    9343 = 29*322 + 5; hence not 29 divides 9343 by NAT_4:9;
    9343 = 31*301 + 12; hence not 31 divides 9343 by NAT_4:9;
    9343 = 37*252 + 19; hence not 37 divides 9343 by NAT_4:9;
    9343 = 41*227 + 36; hence not 41 divides 9343 by NAT_4:9;
    9343 = 43*217 + 12; hence not 43 divides 9343 by NAT_4:9;
    9343 = 47*198 + 37; hence not 47 divides 9343 by NAT_4:9;
    9343 = 53*176 + 15; hence not 53 divides 9343 by NAT_4:9;
    9343 = 59*158 + 21; hence not 59 divides 9343 by NAT_4:9;
    9343 = 61*153 + 10; hence not 61 divides 9343 by NAT_4:9;
    9343 = 67*139 + 30; hence not 67 divides 9343 by NAT_4:9;
    9343 = 71*131 + 42; hence not 71 divides 9343 by NAT_4:9;
    9343 = 73*127 + 72; hence not 73 divides 9343 by NAT_4:9;
    9343 = 79*118 + 21; hence not 79 divides 9343 by NAT_4:9;
    9343 = 83*112 + 47; hence not 83 divides 9343 by NAT_4:9;
    9343 = 89*104 + 87; hence not 89 divides 9343 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9343 & n is prime
  holds not n divides 9343 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
