
theorem
  3323 is prime
proof
  now
    3323 = 2*1661 + 1; hence not 2 divides 3323 by NAT_4:9;
    3323 = 3*1107 + 2; hence not 3 divides 3323 by NAT_4:9;
    3323 = 5*664 + 3; hence not 5 divides 3323 by NAT_4:9;
    3323 = 7*474 + 5; hence not 7 divides 3323 by NAT_4:9;
    3323 = 11*302 + 1; hence not 11 divides 3323 by NAT_4:9;
    3323 = 13*255 + 8; hence not 13 divides 3323 by NAT_4:9;
    3323 = 17*195 + 8; hence not 17 divides 3323 by NAT_4:9;
    3323 = 19*174 + 17; hence not 19 divides 3323 by NAT_4:9;
    3323 = 23*144 + 11; hence not 23 divides 3323 by NAT_4:9;
    3323 = 29*114 + 17; hence not 29 divides 3323 by NAT_4:9;
    3323 = 31*107 + 6; hence not 31 divides 3323 by NAT_4:9;
    3323 = 37*89 + 30; hence not 37 divides 3323 by NAT_4:9;
    3323 = 41*81 + 2; hence not 41 divides 3323 by NAT_4:9;
    3323 = 43*77 + 12; hence not 43 divides 3323 by NAT_4:9;
    3323 = 47*70 + 33; hence not 47 divides 3323 by NAT_4:9;
    3323 = 53*62 + 37; hence not 53 divides 3323 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3323 & n is prime
  holds not n divides 3323 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
