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I don't know if my comment is a contribution for your nice question (I'm an amateur, feel free to add a comment if it doesn't fit with your question), I know an article from the Spanish version of the journal Scientific American that is Investigación y Ciencia, I say the column by Bartolo Luque Juegos matemáticos, the article is Un nuevo patrón en los números primos, Investigación y Ciencia (Julio 2019). I don't know the research article Bartolo Luque and Lucas Lacasa, The First-Digit Frequencies of Prime Numbers and Riemann Zeta Zeros, Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 465, No. 2107 (Jul. 8, 2009), Royal Society. Thus I don't know if it have been inspired by computational search or experimentations, or if there are more reasonings in such article.