Have you figured out that Modern Physics problem yet? Just Kidding...Good to hear from you.
Here are your boundary conditions:
Time available: 3(1016)sec.
Material available: 109 primordial pools.
Task: Assemble 0.0001% of a genetic chain for a prime organism with time for geometric growth.
Assumptions: (1) Amoeba proteus with 2.9(1011) base pairs would be a representative prime organism. (2) A geometric growth curve will account for increasing genetic replicative efficiencies. (3) Pairing trials would occur every second. (4) Geometries and distinct assemblies give each trial a success rate of 20%. (5) Only four distinct sugars need be considered.
The rest is statistical mechanics...
How many universes are allowed? You didn't specify that.
3(1016)sec
A number you've simply invented. That translates to 951,293,759 years. The age of the earth is known to be 4.55 billion years, and the very oldest fossils are 3 billion years old. You have no way of knowing when during that 1.55 billion year period before known fossils life arose, and hence no justification whatsoever for cutting the available time by 1/3'rd. This is a habit I notice you've engaged in consistently, stacking the deck to manipulate your way to a predetermined outcome. But I digress...
Material available: 109 primordial pools
Another number you've simply invented - based on what, I haven't a clue. Given the size of the earth, there are millions, if not billions, of potential locations for life to have begun right here on this planet, without invoking the size of the universe or some such nonsense. Nobody suggests that each trial took place one single place in sequence, so insofar as you're suggesting that only one place on earth was available for such development, you're arguing against a model that you've simply invented out of whole cloth. Parallelism is widely understood as one of the mechanisms you've - conveniently, I note - overlooked.
Task: Assemble 0.0001% of a genetic chain for a prime organism with time for geometric growth
Why? You've offered no justification for using this percentage over any other. Why not 0.01%? Why not 0.0000001%? And 0.0001% of what, exactly? Well, that's where the dissembling just becomes exceedingly silly:
Assumptions: (1) Amoeba proteus with 2.9(1011) base pairs would be a representative prime organism
LOL. Oh, I see. We want 0.0001% of one of the largest genomes in existence! LOL - how very, very convenient. You point to an organism with a genome of 290 billion base pairs as "representative"? How on earth can you possibly justify that? Humans have, for crying out loud, a genome that's 1% the size of A. proteus, at 2.9 billion base pairs, but 290 billion is supposed to be "representative" of early life. Why not M. pneumoniae? That organism has a genome of only 800,000 base pairs - why not make that "representative"? Because it doesn't properly stack the deck, I suspect.
LOL - bring out the hook, and bring me someone who knows what they're doing.
(2) A geometric growth curve will account for increasing genetic replicative efficiencies.
Sez who? You? Based on what? Why not allow for natural selection to account for that? That is what the actual theory of evolution says, after all.
Pairing trials would occur every second....Geometries and distinct assemblies give each trial a success rate of 20%
Why? Why not every ten seconds? Why not every millisecond? Why not a success rate of 40%? 4%? Why invent numbers - again - with no basis in reality whatsoever?
The rest is statistical mechanics...
No, it's pure garbage. You put garbage numbers in, and you get garbage numbers out, and it really doesn't matter what you do to manipulate them in between those two events - you can polish that turd until your arm falls off, but it's never going to be anything more than that.
Since you are ignoring the laws of thermodynamics and chemical reactions, you are out to lunch.