
theorem
  2713 is prime
proof
  now
    2713 = 2*1356 + 1; hence not 2 divides 2713 by NAT_4:9;
    2713 = 3*904 + 1; hence not 3 divides 2713 by NAT_4:9;
    2713 = 5*542 + 3; hence not 5 divides 2713 by NAT_4:9;
    2713 = 7*387 + 4; hence not 7 divides 2713 by NAT_4:9;
    2713 = 11*246 + 7; hence not 11 divides 2713 by NAT_4:9;
    2713 = 13*208 + 9; hence not 13 divides 2713 by NAT_4:9;
    2713 = 17*159 + 10; hence not 17 divides 2713 by NAT_4:9;
    2713 = 19*142 + 15; hence not 19 divides 2713 by NAT_4:9;
    2713 = 23*117 + 22; hence not 23 divides 2713 by NAT_4:9;
    2713 = 29*93 + 16; hence not 29 divides 2713 by NAT_4:9;
    2713 = 31*87 + 16; hence not 31 divides 2713 by NAT_4:9;
    2713 = 37*73 + 12; hence not 37 divides 2713 by NAT_4:9;
    2713 = 41*66 + 7; hence not 41 divides 2713 by NAT_4:9;
    2713 = 43*63 + 4; hence not 43 divides 2713 by NAT_4:9;
    2713 = 47*57 + 34; hence not 47 divides 2713 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2713 & n is prime
  holds not n divides 2713 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
