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How many generation estimated from first cell to modern human?

I was trying to find the answer to this question while thinking of just how many generational iterations there have been to the genome from the first cell to me, to see just how many mutations would be needed to have changed it. Does anyone here, Dawkins included, have any sort of ball park number?

I would imagine it would be easier to break it down by each species, so to speak. In other words, given the current rate of reproduction (about 4 generations per century) and the known time of the first homo sapiens (where probably the century average was higher at 5 or 6 generations), how many members are in my lineage?

Then do the same calculation back to the first primate, mammal (circumvent lizards and birds), the first synapsid, tetrapod, vertabrate, etc. all the way down to microbes reproducing several times daily. Has such a number ever been postulated, systematically worked out as best we can estimate based on the reproductive lifespan of each life form and how long it existed before branching into something else and what ultimately led to us?

Many thanks to whoever can accomplish this one!


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