
theorem
  3389 is prime
proof
  now
    3389 = 2*1694 + 1; hence not 2 divides 3389 by NAT_4:9;
    3389 = 3*1129 + 2; hence not 3 divides 3389 by NAT_4:9;
    3389 = 5*677 + 4; hence not 5 divides 3389 by NAT_4:9;
    3389 = 7*484 + 1; hence not 7 divides 3389 by NAT_4:9;
    3389 = 11*308 + 1; hence not 11 divides 3389 by NAT_4:9;
    3389 = 13*260 + 9; hence not 13 divides 3389 by NAT_4:9;
    3389 = 17*199 + 6; hence not 17 divides 3389 by NAT_4:9;
    3389 = 19*178 + 7; hence not 19 divides 3389 by NAT_4:9;
    3389 = 23*147 + 8; hence not 23 divides 3389 by NAT_4:9;
    3389 = 29*116 + 25; hence not 29 divides 3389 by NAT_4:9;
    3389 = 31*109 + 10; hence not 31 divides 3389 by NAT_4:9;
    3389 = 37*91 + 22; hence not 37 divides 3389 by NAT_4:9;
    3389 = 41*82 + 27; hence not 41 divides 3389 by NAT_4:9;
    3389 = 43*78 + 35; hence not 43 divides 3389 by NAT_4:9;
    3389 = 47*72 + 5; hence not 47 divides 3389 by NAT_4:9;
    3389 = 53*63 + 50; hence not 53 divides 3389 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3389 & n is prime
  holds not n divides 3389 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
