
theorem
  3329 is prime
proof
  now
    3329 = 2*1664 + 1; hence not 2 divides 3329 by NAT_4:9;
    3329 = 3*1109 + 2; hence not 3 divides 3329 by NAT_4:9;
    3329 = 5*665 + 4; hence not 5 divides 3329 by NAT_4:9;
    3329 = 7*475 + 4; hence not 7 divides 3329 by NAT_4:9;
    3329 = 11*302 + 7; hence not 11 divides 3329 by NAT_4:9;
    3329 = 13*256 + 1; hence not 13 divides 3329 by NAT_4:9;
    3329 = 17*195 + 14; hence not 17 divides 3329 by NAT_4:9;
    3329 = 19*175 + 4; hence not 19 divides 3329 by NAT_4:9;
    3329 = 23*144 + 17; hence not 23 divides 3329 by NAT_4:9;
    3329 = 29*114 + 23; hence not 29 divides 3329 by NAT_4:9;
    3329 = 31*107 + 12; hence not 31 divides 3329 by NAT_4:9;
    3329 = 37*89 + 36; hence not 37 divides 3329 by NAT_4:9;
    3329 = 41*81 + 8; hence not 41 divides 3329 by NAT_4:9;
    3329 = 43*77 + 18; hence not 43 divides 3329 by NAT_4:9;
    3329 = 47*70 + 39; hence not 47 divides 3329 by NAT_4:9;
    3329 = 53*62 + 43; hence not 53 divides 3329 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3329 & n is prime
  holds not n divides 3329 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
