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Mar 31, 2020 at 20:34 comment added Robert Israel Agreed, it's not really random, but a random model can give useful heuristics, as with Cramér's random model for the primes.
Mar 31, 2020 at 7:13 comment added WhatsUp Nice answer. Although the "matter of randomness" actually involves nothing random...
Mar 31, 2020 at 6:45 comment added user153451 I have found some $k$ for which for some small $m$ it seems that there is no $p$ such that $\varphi(pm+k)=\varphi(pm+p+k)$ but both such $k$ and $m$ seem to be very rare.
Mar 31, 2020 at 2:31 history answered Robert Israel CC BY-SA 4.0