
theorem
  2731 is prime
proof
  now
    2731 = 2*1365 + 1; hence not 2 divides 2731 by NAT_4:9;
    2731 = 3*910 + 1; hence not 3 divides 2731 by NAT_4:9;
    2731 = 5*546 + 1; hence not 5 divides 2731 by NAT_4:9;
    2731 = 7*390 + 1; hence not 7 divides 2731 by NAT_4:9;
    2731 = 11*248 + 3; hence not 11 divides 2731 by NAT_4:9;
    2731 = 13*210 + 1; hence not 13 divides 2731 by NAT_4:9;
    2731 = 17*160 + 11; hence not 17 divides 2731 by NAT_4:9;
    2731 = 19*143 + 14; hence not 19 divides 2731 by NAT_4:9;
    2731 = 23*118 + 17; hence not 23 divides 2731 by NAT_4:9;
    2731 = 29*94 + 5; hence not 29 divides 2731 by NAT_4:9;
    2731 = 31*88 + 3; hence not 31 divides 2731 by NAT_4:9;
    2731 = 37*73 + 30; hence not 37 divides 2731 by NAT_4:9;
    2731 = 41*66 + 25; hence not 41 divides 2731 by NAT_4:9;
    2731 = 43*63 + 22; hence not 43 divides 2731 by NAT_4:9;
    2731 = 47*58 + 5; hence not 47 divides 2731 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2731 & n is prime
  holds not n divides 2731 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
