
theorem
  3217 is prime
proof
  now
    3217 = 2*1608 + 1; hence not 2 divides 3217 by NAT_4:9;
    3217 = 3*1072 + 1; hence not 3 divides 3217 by NAT_4:9;
    3217 = 5*643 + 2; hence not 5 divides 3217 by NAT_4:9;
    3217 = 7*459 + 4; hence not 7 divides 3217 by NAT_4:9;
    3217 = 11*292 + 5; hence not 11 divides 3217 by NAT_4:9;
    3217 = 13*247 + 6; hence not 13 divides 3217 by NAT_4:9;
    3217 = 17*189 + 4; hence not 17 divides 3217 by NAT_4:9;
    3217 = 19*169 + 6; hence not 19 divides 3217 by NAT_4:9;
    3217 = 23*139 + 20; hence not 23 divides 3217 by NAT_4:9;
    3217 = 29*110 + 27; hence not 29 divides 3217 by NAT_4:9;
    3217 = 31*103 + 24; hence not 31 divides 3217 by NAT_4:9;
    3217 = 37*86 + 35; hence not 37 divides 3217 by NAT_4:9;
    3217 = 41*78 + 19; hence not 41 divides 3217 by NAT_4:9;
    3217 = 43*74 + 35; hence not 43 divides 3217 by NAT_4:9;
    3217 = 47*68 + 21; hence not 47 divides 3217 by NAT_4:9;
    3217 = 53*60 + 37; hence not 53 divides 3217 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3217 & n is prime
  holds not n divides 3217 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
