
theorem
  8741 is prime
proof
  now
    8741 = 2*4370 + 1; hence not 2 divides 8741 by NAT_4:9;
    8741 = 3*2913 + 2; hence not 3 divides 8741 by NAT_4:9;
    8741 = 5*1748 + 1; hence not 5 divides 8741 by NAT_4:9;
    8741 = 7*1248 + 5; hence not 7 divides 8741 by NAT_4:9;
    8741 = 11*794 + 7; hence not 11 divides 8741 by NAT_4:9;
    8741 = 13*672 + 5; hence not 13 divides 8741 by NAT_4:9;
    8741 = 17*514 + 3; hence not 17 divides 8741 by NAT_4:9;
    8741 = 19*460 + 1; hence not 19 divides 8741 by NAT_4:9;
    8741 = 23*380 + 1; hence not 23 divides 8741 by NAT_4:9;
    8741 = 29*301 + 12; hence not 29 divides 8741 by NAT_4:9;
    8741 = 31*281 + 30; hence not 31 divides 8741 by NAT_4:9;
    8741 = 37*236 + 9; hence not 37 divides 8741 by NAT_4:9;
    8741 = 41*213 + 8; hence not 41 divides 8741 by NAT_4:9;
    8741 = 43*203 + 12; hence not 43 divides 8741 by NAT_4:9;
    8741 = 47*185 + 46; hence not 47 divides 8741 by NAT_4:9;
    8741 = 53*164 + 49; hence not 53 divides 8741 by NAT_4:9;
    8741 = 59*148 + 9; hence not 59 divides 8741 by NAT_4:9;
    8741 = 61*143 + 18; hence not 61 divides 8741 by NAT_4:9;
    8741 = 67*130 + 31; hence not 67 divides 8741 by NAT_4:9;
    8741 = 71*123 + 8; hence not 71 divides 8741 by NAT_4:9;
    8741 = 73*119 + 54; hence not 73 divides 8741 by NAT_4:9;
    8741 = 79*110 + 51; hence not 79 divides 8741 by NAT_4:9;
    8741 = 83*105 + 26; hence not 83 divides 8741 by NAT_4:9;
    8741 = 89*98 + 19; hence not 89 divides 8741 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8741 & n is prime
  holds not n divides 8741 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
