On the asymptotic expansion of the sum of the first n primes

Details On the asymptotic expansion of the sum of the first n primes On the asymptotic expansion of the sum of the first n primes

2010-11-07

arxiv.org/abs/1011.1667v1

Mathematics

Number Theory

5 pages, prime numbers, Mandl's inequality, Robin's conjecture

Scientific paper

An asymptotic formula for the sum of the first n primes is derived. This
result improves the previous results of P. Dusart. Using this asymptotic
expansion, we prove the conjectures of R. Mandl and G. Robin on the upper and
the lower bound of the sum of the first n primes respectively.

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