
theorem
  8467 is prime
proof
  now
    8467 = 2*4233 + 1; hence not 2 divides 8467 by NAT_4:9;
    8467 = 3*2822 + 1; hence not 3 divides 8467 by NAT_4:9;
    8467 = 5*1693 + 2; hence not 5 divides 8467 by NAT_4:9;
    8467 = 7*1209 + 4; hence not 7 divides 8467 by NAT_4:9;
    8467 = 11*769 + 8; hence not 11 divides 8467 by NAT_4:9;
    8467 = 13*651 + 4; hence not 13 divides 8467 by NAT_4:9;
    8467 = 17*498 + 1; hence not 17 divides 8467 by NAT_4:9;
    8467 = 19*445 + 12; hence not 19 divides 8467 by NAT_4:9;
    8467 = 23*368 + 3; hence not 23 divides 8467 by NAT_4:9;
    8467 = 29*291 + 28; hence not 29 divides 8467 by NAT_4:9;
    8467 = 31*273 + 4; hence not 31 divides 8467 by NAT_4:9;
    8467 = 37*228 + 31; hence not 37 divides 8467 by NAT_4:9;
    8467 = 41*206 + 21; hence not 41 divides 8467 by NAT_4:9;
    8467 = 43*196 + 39; hence not 43 divides 8467 by NAT_4:9;
    8467 = 47*180 + 7; hence not 47 divides 8467 by NAT_4:9;
    8467 = 53*159 + 40; hence not 53 divides 8467 by NAT_4:9;
    8467 = 59*143 + 30; hence not 59 divides 8467 by NAT_4:9;
    8467 = 61*138 + 49; hence not 61 divides 8467 by NAT_4:9;
    8467 = 67*126 + 25; hence not 67 divides 8467 by NAT_4:9;
    8467 = 71*119 + 18; hence not 71 divides 8467 by NAT_4:9;
    8467 = 73*115 + 72; hence not 73 divides 8467 by NAT_4:9;
    8467 = 79*107 + 14; hence not 79 divides 8467 by NAT_4:9;
    8467 = 83*102 + 1; hence not 83 divides 8467 by NAT_4:9;
    8467 = 89*95 + 12; hence not 89 divides 8467 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8467 & n is prime
  holds not n divides 8467 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
