
theorem
  3209 is prime
proof
  now
    3209 = 2*1604 + 1; hence not 2 divides 3209 by NAT_4:9;
    3209 = 3*1069 + 2; hence not 3 divides 3209 by NAT_4:9;
    3209 = 5*641 + 4; hence not 5 divides 3209 by NAT_4:9;
    3209 = 7*458 + 3; hence not 7 divides 3209 by NAT_4:9;
    3209 = 11*291 + 8; hence not 11 divides 3209 by NAT_4:9;
    3209 = 13*246 + 11; hence not 13 divides 3209 by NAT_4:9;
    3209 = 17*188 + 13; hence not 17 divides 3209 by NAT_4:9;
    3209 = 19*168 + 17; hence not 19 divides 3209 by NAT_4:9;
    3209 = 23*139 + 12; hence not 23 divides 3209 by NAT_4:9;
    3209 = 29*110 + 19; hence not 29 divides 3209 by NAT_4:9;
    3209 = 31*103 + 16; hence not 31 divides 3209 by NAT_4:9;
    3209 = 37*86 + 27; hence not 37 divides 3209 by NAT_4:9;
    3209 = 41*78 + 11; hence not 41 divides 3209 by NAT_4:9;
    3209 = 43*74 + 27; hence not 43 divides 3209 by NAT_4:9;
    3209 = 47*68 + 13; hence not 47 divides 3209 by NAT_4:9;
    3209 = 53*60 + 29; hence not 53 divides 3209 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3209 & n is prime
  holds not n divides 3209 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
