So, I am looking at a new set of clinchers....tires....I see that they are listed at 700x 20/23/etc. What is the 20+ number mean? What is the "recommended" 20-ish #? I ride spirited club rides, 50miles each outing. I like to keep a light bike, quick and responsive. Right now I use old Michelin Axil Pro's 700x 23...weighing in at 222gms. They have served me welll, 3000 miles, no punctures. Would I be best repeating that size? or is another choice better?
I was going to try the Mich Race Pro or Vict. Corcsa CX( I believe they are called).

The second number is the nominal tire width, in mm. The width you need depends on your weight and riding style. Unless you are quite light, a 20 mm tire is too narrow and will have to be pumped very hard to prevent pinch flats. Nominal tire pressure should be 90-110 psi - if you get pinch flats at 110 psi, then it makes more sense to go to wider tires rather than higher pressures. High tire pressure results in rapid tire wear, uncomfortable ride, poor traction, and effectively no decrease in rolling resistance because the high pressure tire is "bouncing back" every time it hits a road imperfection. There are good tires out there from Continental, Vredestein, Michelin, Vittoria, etc.

23mm is a nice middle of the road width, pretty much can't go wrong with it. I ride those most of the time then switch to 24/25mm in the winter when there is more crud on the road. 25mm could be too wide if you have a bike with really short stays or if you are running fenders. It is easy to predict trouble, however, by checking the amount of clearance between your rear tire and your seat tube.

Alan, Those Michelin tires that you are riding have impressed me with their extraordinarily low rolling resistance.

I was shopping for and testing tires that are:
1) race worthy
2) no flats

That's because I have to change the flats myself.

Of those I tested AND of those I reviewed, the Michelin was in the 100 percentile. That's right, the fastest of their class (puncture-free race tires).

I went with the runner up, which was slower but with the additional feature of high-speed cornering in the rain.
That's because I just love to train in the rain. You can't get hot. ;)

Anyway, I'd certainly suggest that you replace with the exact Michelin tire that already served you so well.

If you like the ride of the 23, then by all means replenish with the 23--exact same tire. This size is good for carbon fiber, for steel, and for carbon aluminum mixed frames.

However, if you find that the ride is like being "blasted" then replinish with the 25--exact same tire, larger size.
This size and the next size up is good for extremely rigid frames that make your hands numb and rear end sore. In the case of a bike that "blasts" you, the larger tire will not slow it down.

However, a larger tire will slow down a carbon fiber bike unless the rear spoke tension is increased to compensate the energy loss. This is not usually possible with the "botique" wheels that come with carbon bikes, so stick with the small sizes if your bike is all-carbon.

For this reason, many people use a mixed approach with a small hard tire on the back to increase the energy transmitted from you to the road (that same 23mm you have) and a slightly larger tire (25-27mm) on the front with a lower air pressure to decrease the energy transmitted (bump bump bump--decrease it). This approach works well if you experience arm pain because of a, perhaps, overly-areodynamic riding position.

New wheels can also make huge differences in the ride of a bike.
Rim widths, flexability (or not), and character are just as important as tire selection. The ideal combination provides a shock-free ride with extremely minimized rolling resistance. However, "ideal" is specific to your individual application.

Well, your question did involve all of that, but since you did not mention ride quality, I'd suggest to go right out and buy another set exactly like the ones you've been using. They are excellent and fast.