They promote roughly 500 per year so about 4 years

More like 400 per year.

The 2013 test was given October 2013 I believe. They didn't start promoting off that exam till Jan 2016 if I'm not mistaken. The test prior to that (2011) had I think around 1800. It didn't finish till nov 2015. In my opinion they gave the 2013 test a tad early. It's wrong to make people wait that long before promoting, but they don't ask for my opinion and people with a higher pay grade then me make the decisions. Anyways since dec'15/Jan'16 till now they've gone through @500+ list numbers. With more and more recruits coming in and the NCO program there is gonna be a need for more SGTs (department likes to keep an 8/1 ratio if possible) and with a Sgt contract coming to an end soon (1-2 years I believe) you'll see more Sgt's retire, if they have he time to retire. Now as far as largest list I thought the 2011 test, @1800, was large. But I've heard of an exam being over 2,000. It used to be that the department need a certain amt of Sgt's and had the list stopped at a certain number no matter what the score was. So you could've gotten a 60 and still been promoted.

yes that was the 2003 Sgt test. That was the test that changed the future of where you needed a 70 to make the list I think they went into the high 50's on that list. It was also the last exam where they gave 2.5 points for being a resident of NYC. Lots have changed. Just like the 06 Lt exam which had about 1000 people on it. That list got cut. That's the only exam I know of in the last 18 years that has gotten cut at the 4 year mark.