Why unpopular? You wrote "can identify primes 99.999% of the time for quicker testing", which shows several fundamental and basic flaws in your understanding.
We've had approximate primarily testing methods for a long time and they are quite effective. See https://primes.utm.edu/notes/prp_prob.html (citing https://www.ams.org/journals/mcom/1989-53-188/S0025-5718-198... ), for a 100,000-digit number the odds of Fermat's test for compositeness being a false is 1.3E-10584, which is 99.9999999999999{insert 560 nines here}999999999%.
This is why, in the AMS paper cited as [1] in this link, Dubner wrote "it is virtually certain that R49081 is prime." The full context is:
> In September 1999, it was discovered that R49081 is a probable prime. This was verified on several different computers with different software. Although it is virtually certain that R49081 is prime, it is necessary to prove rigorously that it is prime.
A 99.999%-likely test is far less virtually certain than the test used, and in any case doesn't achieve the goal of rigorously proving it's prime.
Even worse, these standard primality testing methods have a 0% false negative rate, while your hypothetical AI might miss actual repunits even with a 0.000001% rate.
> just a form of embedded randomness, behind any irrational number like Pi
This doesn't makes sense. There are irrational numbers with no randomness, like Liouville's constant and the Champernowne constant. And there are plenty of patterns in primes - the Ulam spiral Wikipedia entry even compares the clearly apparent structure of that spiral to a random distribution, at https://en.wikipedia.org/wiki/Ulam_spiral .
Your comment therefore comes across as very ill-informed, and your doubling down doesn't help.