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Nov 1, 2023 at 14:43 comment added Michael Lugo The paper that Wojowu linked to starts out by saying "if you look at the data, it will look like this is false" (and then goes on to explain where those biases come from). I mention this because my first instinct was to write some code to test this statement up to $10^6$ or so and from the data it looked false to me.
Feb 14, 2022 at 15:27 comment added Joshua Stucky You might also have a look at "prime constellations." It's not exactly what you're asking about, but the concepts are somewhat related.
Feb 14, 2022 at 13:27 comment added Wojowu Conjecturally the answer should be "yes", but I do also doubt this is known unconditionally. Certain biases are expected), but the ultimate asymptotics should be the same. See that paper also for known partial results.
Feb 14, 2022 at 13:17 history asked Jakub Konieczny CC BY-SA 4.0