
theorem
  2729 is prime
proof
  now
    2729 = 2*1364 + 1; hence not 2 divides 2729 by NAT_4:9;
    2729 = 3*909 + 2; hence not 3 divides 2729 by NAT_4:9;
    2729 = 5*545 + 4; hence not 5 divides 2729 by NAT_4:9;
    2729 = 7*389 + 6; hence not 7 divides 2729 by NAT_4:9;
    2729 = 11*248 + 1; hence not 11 divides 2729 by NAT_4:9;
    2729 = 13*209 + 12; hence not 13 divides 2729 by NAT_4:9;
    2729 = 17*160 + 9; hence not 17 divides 2729 by NAT_4:9;
    2729 = 19*143 + 12; hence not 19 divides 2729 by NAT_4:9;
    2729 = 23*118 + 15; hence not 23 divides 2729 by NAT_4:9;
    2729 = 29*94 + 3; hence not 29 divides 2729 by NAT_4:9;
    2729 = 31*88 + 1; hence not 31 divides 2729 by NAT_4:9;
    2729 = 37*73 + 28; hence not 37 divides 2729 by NAT_4:9;
    2729 = 41*66 + 23; hence not 41 divides 2729 by NAT_4:9;
    2729 = 43*63 + 20; hence not 43 divides 2729 by NAT_4:9;
    2729 = 47*58 + 3; hence not 47 divides 2729 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2729 & n is prime
  holds not n divides 2729 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
