
theorem
  4813 is prime
proof
  now
    4813 = 2*2406 + 1; hence not 2 divides 4813 by NAT_4:9;
    4813 = 3*1604 + 1; hence not 3 divides 4813 by NAT_4:9;
    4813 = 5*962 + 3; hence not 5 divides 4813 by NAT_4:9;
    4813 = 7*687 + 4; hence not 7 divides 4813 by NAT_4:9;
    4813 = 11*437 + 6; hence not 11 divides 4813 by NAT_4:9;
    4813 = 13*370 + 3; hence not 13 divides 4813 by NAT_4:9;
    4813 = 17*283 + 2; hence not 17 divides 4813 by NAT_4:9;
    4813 = 19*253 + 6; hence not 19 divides 4813 by NAT_4:9;
    4813 = 23*209 + 6; hence not 23 divides 4813 by NAT_4:9;
    4813 = 29*165 + 28; hence not 29 divides 4813 by NAT_4:9;
    4813 = 31*155 + 8; hence not 31 divides 4813 by NAT_4:9;
    4813 = 37*130 + 3; hence not 37 divides 4813 by NAT_4:9;
    4813 = 41*117 + 16; hence not 41 divides 4813 by NAT_4:9;
    4813 = 43*111 + 40; hence not 43 divides 4813 by NAT_4:9;
    4813 = 47*102 + 19; hence not 47 divides 4813 by NAT_4:9;
    4813 = 53*90 + 43; hence not 53 divides 4813 by NAT_4:9;
    4813 = 59*81 + 34; hence not 59 divides 4813 by NAT_4:9;
    4813 = 61*78 + 55; hence not 61 divides 4813 by NAT_4:9;
    4813 = 67*71 + 56; hence not 67 divides 4813 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4813 & n is prime
  holds not n divides 4813 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
