
theorem
  4493 is prime
proof
  now
    4493 = 2*2246 + 1; hence not 2 divides 4493 by NAT_4:9;
    4493 = 3*1497 + 2; hence not 3 divides 4493 by NAT_4:9;
    4493 = 5*898 + 3; hence not 5 divides 4493 by NAT_4:9;
    4493 = 7*641 + 6; hence not 7 divides 4493 by NAT_4:9;
    4493 = 11*408 + 5; hence not 11 divides 4493 by NAT_4:9;
    4493 = 13*345 + 8; hence not 13 divides 4493 by NAT_4:9;
    4493 = 17*264 + 5; hence not 17 divides 4493 by NAT_4:9;
    4493 = 19*236 + 9; hence not 19 divides 4493 by NAT_4:9;
    4493 = 23*195 + 8; hence not 23 divides 4493 by NAT_4:9;
    4493 = 29*154 + 27; hence not 29 divides 4493 by NAT_4:9;
    4493 = 31*144 + 29; hence not 31 divides 4493 by NAT_4:9;
    4493 = 37*121 + 16; hence not 37 divides 4493 by NAT_4:9;
    4493 = 41*109 + 24; hence not 41 divides 4493 by NAT_4:9;
    4493 = 43*104 + 21; hence not 43 divides 4493 by NAT_4:9;
    4493 = 47*95 + 28; hence not 47 divides 4493 by NAT_4:9;
    4493 = 53*84 + 41; hence not 53 divides 4493 by NAT_4:9;
    4493 = 59*76 + 9; hence not 59 divides 4493 by NAT_4:9;
    4493 = 61*73 + 40; hence not 61 divides 4493 by NAT_4:9;
    4493 = 67*67 + 4; hence not 67 divides 4493 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4493 & n is prime
  holds not n divides 4493 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
