
theorem
  8447 is prime
proof
  now
    8447 = 2*4223 + 1; hence not 2 divides 8447 by NAT_4:9;
    8447 = 3*2815 + 2; hence not 3 divides 8447 by NAT_4:9;
    8447 = 5*1689 + 2; hence not 5 divides 8447 by NAT_4:9;
    8447 = 7*1206 + 5; hence not 7 divides 8447 by NAT_4:9;
    8447 = 11*767 + 10; hence not 11 divides 8447 by NAT_4:9;
    8447 = 13*649 + 10; hence not 13 divides 8447 by NAT_4:9;
    8447 = 17*496 + 15; hence not 17 divides 8447 by NAT_4:9;
    8447 = 19*444 + 11; hence not 19 divides 8447 by NAT_4:9;
    8447 = 23*367 + 6; hence not 23 divides 8447 by NAT_4:9;
    8447 = 29*291 + 8; hence not 29 divides 8447 by NAT_4:9;
    8447 = 31*272 + 15; hence not 31 divides 8447 by NAT_4:9;
    8447 = 37*228 + 11; hence not 37 divides 8447 by NAT_4:9;
    8447 = 41*206 + 1; hence not 41 divides 8447 by NAT_4:9;
    8447 = 43*196 + 19; hence not 43 divides 8447 by NAT_4:9;
    8447 = 47*179 + 34; hence not 47 divides 8447 by NAT_4:9;
    8447 = 53*159 + 20; hence not 53 divides 8447 by NAT_4:9;
    8447 = 59*143 + 10; hence not 59 divides 8447 by NAT_4:9;
    8447 = 61*138 + 29; hence not 61 divides 8447 by NAT_4:9;
    8447 = 67*126 + 5; hence not 67 divides 8447 by NAT_4:9;
    8447 = 71*118 + 69; hence not 71 divides 8447 by NAT_4:9;
    8447 = 73*115 + 52; hence not 73 divides 8447 by NAT_4:9;
    8447 = 79*106 + 73; hence not 79 divides 8447 by NAT_4:9;
    8447 = 83*101 + 64; hence not 83 divides 8447 by NAT_4:9;
    8447 = 89*94 + 81; hence not 89 divides 8447 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8447 & n is prime
  holds not n divides 8447 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
