
theorem
  8243 is prime
proof
  now
    8243 = 2*4121 + 1; hence not 2 divides 8243 by NAT_4:9;
    8243 = 3*2747 + 2; hence not 3 divides 8243 by NAT_4:9;
    8243 = 5*1648 + 3; hence not 5 divides 8243 by NAT_4:9;
    8243 = 7*1177 + 4; hence not 7 divides 8243 by NAT_4:9;
    8243 = 11*749 + 4; hence not 11 divides 8243 by NAT_4:9;
    8243 = 13*634 + 1; hence not 13 divides 8243 by NAT_4:9;
    8243 = 17*484 + 15; hence not 17 divides 8243 by NAT_4:9;
    8243 = 19*433 + 16; hence not 19 divides 8243 by NAT_4:9;
    8243 = 23*358 + 9; hence not 23 divides 8243 by NAT_4:9;
    8243 = 29*284 + 7; hence not 29 divides 8243 by NAT_4:9;
    8243 = 31*265 + 28; hence not 31 divides 8243 by NAT_4:9;
    8243 = 37*222 + 29; hence not 37 divides 8243 by NAT_4:9;
    8243 = 41*201 + 2; hence not 41 divides 8243 by NAT_4:9;
    8243 = 43*191 + 30; hence not 43 divides 8243 by NAT_4:9;
    8243 = 47*175 + 18; hence not 47 divides 8243 by NAT_4:9;
    8243 = 53*155 + 28; hence not 53 divides 8243 by NAT_4:9;
    8243 = 59*139 + 42; hence not 59 divides 8243 by NAT_4:9;
    8243 = 61*135 + 8; hence not 61 divides 8243 by NAT_4:9;
    8243 = 67*123 + 2; hence not 67 divides 8243 by NAT_4:9;
    8243 = 71*116 + 7; hence not 71 divides 8243 by NAT_4:9;
    8243 = 73*112 + 67; hence not 73 divides 8243 by NAT_4:9;
    8243 = 79*104 + 27; hence not 79 divides 8243 by NAT_4:9;
    8243 = 83*99 + 26; hence not 83 divides 8243 by NAT_4:9;
    8243 = 89*92 + 55; hence not 89 divides 8243 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8243 & n is prime
  holds not n divides 8243 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
