I've been thinking about this recently as I'm about to switch up my ratio. Is it ideal to chose a prime number front chain ring and then adjust the back to whatever based on the actual ratio you want? Selecting the largest reasonable prime for a front chain ring allows you to choose a larger rear cog, which will give you more skid patches, so your rear tire will last longer. Is this a good idea? It seems like it's the most flexible option. I'm sure this is old news but, it's just something I've been thinking about as I see lots of 52T and 48T chain rings.

42/16. 71 gear inches (high enough to go fast, low enough to climb), 8 skid patches, even teeth for maximum chain and cog life.

anything ending in 17 or 19... prime number skid patches.

or 53x11 brakeless unless you're a *****.

This breaks if your front chain ring is a multiple of your rear cog, 51 (17*3) is most likely. I realize that's rare, but what's the harm in padding your lead and just sticking with a prime front chain ring, then if you want to change your rear cog, you don't have to worry about anything else but ratio, you won't be accidentally dropping to 2 or 3 skid patches.

Yes, your initial idea is correct. Put a prime in the front and then forget about the skid patches. However, as I said, you don't need that many unless you skid perfectly locked every time. For example, if you back pedal at all to slow down faster when you skid, you're spinning the tire through a much larger area than just the initial skid patch, so at some point your patches all overlap. It's been estimated that this happens around 8 or 9, but your mileage may vary.

In any case, if you're changing your cog all the time, go for a prime in the front. Otherwise, search for "odd number chainring" or read Sheldon's page about the possible benefits of even numbers of teeth. It doesn't take much to figure out skid patches, so there really isn't much benefit of a "set it and forget it" arrangement based on skid patches.

In my flat city 44x17 is perfect for me. Lots of skid patches and a good all around gear.

just use a 17t cog and any chainring except for 51 or 34 and then you will have 17 skid patches for pretty much perfectly even wear all the way around the tire

Skid patches are for underwear.

Just rotate the tires from time to time and run the GI you want to run.
I use 48x18T in both fixed and freewheel.

52 X 16
42 X 13
Both are about 85 G-in
Mostly flat daily commute 25 mi each way.

Prime up front and then whatever you want in back.

49:18 - bad ass. Great gearing for the city and 18 skid patches.

Not to mention you can go 49:15 for track without a new chain.

I was running that. Spinning's great although I have a lot of lonnnnnnng stretches to work and it gets a bit boring.

That's what I'm saying. I'm not really asking what's the best ratio, that's 100% personal. I'm saying theoretically, in order to attain the perfect ratio for yourself without destroying your tires, you should have a prime chain ring.

It's a good compromise gear for the hills. I was running 48x16T which makes hills over 5% impossible.

Good point but not everyone is out too get 18 discrete skid patches. I have found that my 3 patches is enough for regular wear so long as I rotate the tire from time to time.