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math.NT2025
On the arithmetic average of the first primes
Matt Visser
The arithmetic average of the first primes, , exhibits very many interesting and subtle properties. Since the transformation from $p_n \…
math.NT2025
The n-th prime exponentially
Matt Visser
From known effective bounds on the prime counting function of the form \[ |π(x)-\mathrm{Li}(x)| < a \;x \;(\ln x)^{b} \; \exp\left(-{c}\; \sqrt{\ln x}\right); \qquad (x \geq x_0);…