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I expect very large error bars, but what's the number of generations between the very first lifeform (that can be described as evolving in generations) and humans? Is it closer to a quadrillion or a trillion?

A related answer estimates that there were around 300,000 generations between us and the chimp/human common ancestor.

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The generations that preceded multicellular life will so vastly dominate the answer that the last 500,000,000 years don't even matter. So life is 3.5 billion years old, and for most of this time, life was prokaryotic, dividing every 20 minutes or so. Thats 26,000 generations per year. Multiply that by 3.5 billion and you get 9 trillion generations. That is likely an overestimate, based on optimal growing conditions of bacterial in exponential growth. But it is unlikely to be orders of magnitude off.

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    $\begingroup$ eukaryotes have been around for ~2.7 billion years so this should be taken with a large margin of error. Also we don't know how fast the earliest life reproduced, but it is probably accurate within one or two orders of magnitude. $\endgroup$
    – John
    Commented Nov 17, 2017 at 0:40
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    $\begingroup$ prokaryotes often make clones, so their generations are of a different kind. $\endgroup$
    – bandybabboon
    Commented Nov 17, 2017 at 11:45
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    $\begingroup$ We cannot be sure that the earliest life forms had well defined generations. It must have taken eons to learn replicating regularly. It is not even given that the life emerged just once and that we descend directly from the earliest organisms. $\endgroup$
    – jmster
    Commented Nov 17, 2017 at 18:05
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    $\begingroup$ Yan Wong and Richard Dawkins estimate the number of generations between modern humans and common ancestors of clades going back to the first life form in the book The Ancestor's Tale. Each chapter begins with such an estimation, for each clade as you descend down ("back in time") to the last common ancestors of each consequent clade. However, even they woefully give up after a while. There's just no way to estimate it beyond a certain point, past the metazoan clade, because it just doesn't make sense to speculate without basis anymore. Any attempted error margins will very necessarily be huge. $\endgroup$
    – S Pr
    Commented May 18, 2022 at 12:10
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    $\begingroup$ I would also mention that we switch definition of 'generations' at some point to even attempt to answer this question. For humans, a parent is 1 generation back. For cells, it is a division into daughter cells whereby there is no parent, only two "sister" cells that come from an originating cell ("mother cell", though this is a misleading term given the prior context). I too disagree with the estimation of a 20 minute division time, I don't think that's close to the reality of it. At least, it's a projection based on best-possible time for extant microbes, which is a stretch. $\endgroup$
    – S Pr
    Commented May 18, 2022 at 12:16

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