yeah that sounds about right for a sax too, alto at least
what is the lowest you can get?
I can only get down to an F# below the staff, but when you have really nice lip control you can go down a whole other octave. Then there's pedal tones, it's as low as a tuba, but it sounds like unintelligible garbage.
My mouthpiece is a 7c. I'm blowing steady, strong air, tight lips, and not too much pressure. But it blows my chops every time.
I'd highly recommend a 3c then.
Make sure your lips aren't too tight, as well. If they are your lips won't be able to vibrate as fast, and the sound won't come out. It's good you aren't putting pressure, that's a great habit many players don't have.