
theorem
  3221 is prime
proof
  now
    3221 = 2*1610 + 1; hence not 2 divides 3221 by NAT_4:9;
    3221 = 3*1073 + 2; hence not 3 divides 3221 by NAT_4:9;
    3221 = 5*644 + 1; hence not 5 divides 3221 by NAT_4:9;
    3221 = 7*460 + 1; hence not 7 divides 3221 by NAT_4:9;
    3221 = 11*292 + 9; hence not 11 divides 3221 by NAT_4:9;
    3221 = 13*247 + 10; hence not 13 divides 3221 by NAT_4:9;
    3221 = 17*189 + 8; hence not 17 divides 3221 by NAT_4:9;
    3221 = 19*169 + 10; hence not 19 divides 3221 by NAT_4:9;
    3221 = 23*140 + 1; hence not 23 divides 3221 by NAT_4:9;
    3221 = 29*111 + 2; hence not 29 divides 3221 by NAT_4:9;
    3221 = 31*103 + 28; hence not 31 divides 3221 by NAT_4:9;
    3221 = 37*87 + 2; hence not 37 divides 3221 by NAT_4:9;
    3221 = 41*78 + 23; hence not 41 divides 3221 by NAT_4:9;
    3221 = 43*74 + 39; hence not 43 divides 3221 by NAT_4:9;
    3221 = 47*68 + 25; hence not 47 divides 3221 by NAT_4:9;
    3221 = 53*60 + 41; hence not 53 divides 3221 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3221 & n is prime
  holds not n divides 3221 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
