
theorem
  1741 is prime
proof
  now
    1741 = 2*870 + 1; hence not 2 divides 1741 by NAT_4:9;
    1741 = 3*580 + 1; hence not 3 divides 1741 by NAT_4:9;
    1741 = 5*348 + 1; hence not 5 divides 1741 by NAT_4:9;
    1741 = 7*248 + 5; hence not 7 divides 1741 by NAT_4:9;
    1741 = 11*158 + 3; hence not 11 divides 1741 by NAT_4:9;
    1741 = 13*133 + 12; hence not 13 divides 1741 by NAT_4:9;
    1741 = 17*102 + 7; hence not 17 divides 1741 by NAT_4:9;
    1741 = 19*91 + 12; hence not 19 divides 1741 by NAT_4:9;
    1741 = 23*75 + 16; hence not 23 divides 1741 by NAT_4:9;
    1741 = 29*60 + 1; hence not 29 divides 1741 by NAT_4:9;
    1741 = 31*56 + 5; hence not 31 divides 1741 by NAT_4:9;
    1741 = 37*47 + 2; hence not 37 divides 1741 by NAT_4:9;
    1741 = 41*42 + 19; hence not 41 divides 1741 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1741 & n is prime
  holds not n divides 1741 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
