Astronomers have just found more than half a million new asteroids

https://arxiv.org/pdf/2108.05749.pdf

This has so much in it

Figure 12 is really cool; I assume that the slots are due to the planets.

Yes, those gaps are caused by orbital resonance. Orbits whose periods are related to Jupiter's by ratios of small integers tend to be unstable over astronomical timescales.

https://en.wikipedia.org/wiki/Kirkwood_gap

Do these changing numbers have a yet quantified influence over the probability of impactor events on Earth?

If we're discovering lots of new asteroids, are our equations underestimating the risk?

How do they figure out if the asteroid has already been seen before or not?

You can have a look here: "4. Identification of known Solar System objects", https://arxiv.org/pdf/2108.05749.pdf#section.4

By the way: you can easily create links like this by opening the document structure view of a PDF in Firefox and by then copying a link to a section via the context menu. If this is not possible for some reason, one could still have used #page=3 to direct the user to a particular page in the PDF at least.

Neat. thanks!

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