In the 90s most people had touched grass, but few touched a computer.

In the 2090s most people will have touched a computer, but not grass.

But at least we'll have fully sentient dildos armed with laser guns to mildly stimulate our mandatory attached cyber-clits, or alternatively annihilate thought criminals.

In other news my prime generator has exhaustively been checked against, all primes from 5 to 1 million. I used miller-rabin with k=40 to confirm the results.

The set the generator creates is the join of the quasi-lucas carmichael numbers, the carmichael numbers, and the primes. So after I generated a number I just had to treat those numbers as 'pollutants' and filter them out, which was dead simple.

Whats left after filtering, is strictly the primes.

I also tested it randomly on 50-55 bit primes, and it always returned true, but that range hasn't been fully tested so far because it takes 9-12 seconds per number at that point.

I was expecting maybe a few failures by my generator. So what I did was I wrote a function, genMillerTest(), and all it does is take some number n, returns the next prime after it (using my functions nextPrime() and isPrime()), and then tests it against miller-rabin. If miller returns false, then I add the result to a list. And then I check *those* results by hand (because miller can occasionally return false positives, though I'm not familiar enough with the math to know how often).

Well, imagine my surprise when I had zero false positives.

Which means either my code is generating the same exact set as miller (under some very large value of n), or the chance of miller (at k=40 tests) returning a false positive is vanishingly small.

My next steps should be to parallelize the checking process, and set up my other desktop to run those tests continuously.
Concurrently I should work on figuring out why my slowest primality tests (theres six of them, though I think I can eliminate two) are so slow and if I can better estimate or derive a pattern that allows faster results by better initialization of the variables used by these tests.

I already wrote some cases to output which tests most frequently succeeded (if any of them pass, then the number isn't prime), and therefore could cut short the primality test of a number. I rewrote the function to put those tests in order from most likely to least likely.

I'm also thinking that there may be some clues for faster computation in other bases, or perhaps in binary, or inspecting the patterns of values in the natural logs of non-primes versus primes. Or even looking into the *execution* time of numbers that successfully pass as prime versus ones that don't. Theres a bevy of possible approaches.

The entire process for the first 1_000_000 numbers, ran 1621.28 seconds, or just shy of a tenth of a second per test but I'm sure thats biased toward the head of the list.

If theres any other approach or ideas I may be overlooking, I wouldn't know where to begin.