
theorem
  1709 is prime
proof
  now
    1709 = 2*854 + 1; hence not 2 divides 1709 by NAT_4:9;
    1709 = 3*569 + 2; hence not 3 divides 1709 by NAT_4:9;
    1709 = 5*341 + 4; hence not 5 divides 1709 by NAT_4:9;
    1709 = 7*244 + 1; hence not 7 divides 1709 by NAT_4:9;
    1709 = 11*155 + 4; hence not 11 divides 1709 by NAT_4:9;
    1709 = 13*131 + 6; hence not 13 divides 1709 by NAT_4:9;
    1709 = 17*100 + 9; hence not 17 divides 1709 by NAT_4:9;
    1709 = 19*89 + 18; hence not 19 divides 1709 by NAT_4:9;
    1709 = 23*74 + 7; hence not 23 divides 1709 by NAT_4:9;
    1709 = 29*58 + 27; hence not 29 divides 1709 by NAT_4:9;
    1709 = 31*55 + 4; hence not 31 divides 1709 by NAT_4:9;
    1709 = 37*46 + 7; hence not 37 divides 1709 by NAT_4:9;
    1709 = 41*41 + 28; hence not 41 divides 1709 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1709 & n is prime
  holds not n divides 1709 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
