
theorem
  1747 is prime
proof
  now
    1747 = 2*873 + 1; hence not 2 divides 1747 by NAT_4:9;
    1747 = 3*582 + 1; hence not 3 divides 1747 by NAT_4:9;
    1747 = 5*349 + 2; hence not 5 divides 1747 by NAT_4:9;
    1747 = 7*249 + 4; hence not 7 divides 1747 by NAT_4:9;
    1747 = 11*158 + 9; hence not 11 divides 1747 by NAT_4:9;
    1747 = 13*134 + 5; hence not 13 divides 1747 by NAT_4:9;
    1747 = 17*102 + 13; hence not 17 divides 1747 by NAT_4:9;
    1747 = 19*91 + 18; hence not 19 divides 1747 by NAT_4:9;
    1747 = 23*75 + 22; hence not 23 divides 1747 by NAT_4:9;
    1747 = 29*60 + 7; hence not 29 divides 1747 by NAT_4:9;
    1747 = 31*56 + 11; hence not 31 divides 1747 by NAT_4:9;
    1747 = 37*47 + 8; hence not 37 divides 1747 by NAT_4:9;
    1747 = 41*42 + 25; hence not 41 divides 1747 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1747 & n is prime
  holds not n divides 1747 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
