I mentioned some asteroid counts in my 2005 description of the work our family has done with asteroids for astrology.
A couple recent milestones prompted me to write this short addendum.
One big change a couple years ago is that the MPC is no longer the publisher of new asteroid names. (Just names moved. The MPC still releases elements & observations.) Starting in May 2021, the publication of new names moved to a site of the Working Group for Small Bodies Nomenclature (WGSBN). The archived bulletins with names and citations are available free at the WGSBN Bulletin Archive.
The WGSBN Bulletin (Volume 3, #6) dated 2023 May 1 with 55 new names brings the total count of named asteroids to a nice round number: 24,000.
Picking up from my 2005 post, named asteroids passed 13,000 in 2006, 14,000 in 2007, 15,000 in 2009, 16,000 in 2010, 17,000 in 2012, 18,000 in 2013, 19,000 in 2015, 20,000 in 2016, 21,000 in 2017, 22,000 in 2020, 23,000 in 2022, and reached 24,000 in the recent WGSBN Bulletin.
A different milestone was in an MPC Update that came out in April (dated April 7, but available on the web later in April). The newly numbered asteroids from the MPC crossed the 620,000 boundary. MPC files with orbital elements or observations have used a 5-character asteroid number for decades. The new numbers in the 2005 October 19 MPC passed the 5-digit limit of asteroid 99999 and started using a form of packed number with A0000 for the next number (100,000). By using A-Z, then a-z in the first character for 10 through 61, they were able to handle numbers up to 619,999 (z9999), a limit they reached in the 2022 November 10 MPC.
Since my programs to integrate asteroid orbits depend on MPC (or another astronomical source such as Lowell) elements to start calculations and MPC observation files to check results, I have been expecting for years to see new file formats with longer asteroid numbers. What the MPC did instead was to take number packing to the next level. The 2023 January 27 MPC had only one new number: ~0000. The 2023 April 7 MPC has new numbers ~0001 through ~001k. I needed to work with some of the April data, so I needed to be able to interpret the new format of packed numbers. I looked around a little and found the MPC Packed Provisional and Permanent Designations page I needed. The new format packs much higher numbers into the same five-character space by making all 4 characters after the ~ base-62 (0-9, A-Z, a-z) and starting from 620,000. The numbers ~0001 through ~001k in the April MPC translate to 620,001 through 620,108.
See my Links of interest page for several MPC and WGSBN page links.