Here is my attempt at a calculation. Disclaimer: this is based on googling. If you are actually knowledgeable in the subject, please step in and set me right.
There are 10^11 neurons in the human brain.
A neuron will fire about 200 times per second.
It should take a constant number of flops to decide whether a neuron will fire —say 10 flops (no need to solve a differential equation, neural networks usually use some discrete heuristics for something like this)
I want a society of 10^6 orcs running for 10^6 years
As you suggest, lets let the simulation run for a year of real time (moving away at this point from my initial suggestion of 1 second). By my calculations, it seems that in order for this to happen we need a computer that does 2x10^25 flops per second.
According to this
...in 2018 we will have a supercomputer that does about 2x10^17 flops per second.
That means we need a computer that is one hundred million times faster than the best computer in 2018.
That is still quite a lot, of course. If Moore’s law was ongoing, this would take ~40 years; but Moore’s law is dying. Still, it is not outside the realm of possibility for, say, the next 100 years.
Edit: By the way, one does not need to literally implement what I suggested—the scheme I suggested is in principle applicable whenever you have a superintelligence, regardless of how it was designed.
Indeed, if we somehow develop an above-human intelligence, rather than trying to make sure its goals are aligned with ours, we might instead let it loose within a simulated world, giving it a preference for continued survival. Just one superintelligence thinking about factoring for a few thousand simulated years would likely be enough to let us factor any number we want. We could even give it have in-simulation ways of modifying its own code.
Right, that is what i meant.