An Improved Bound on the Sum of Prime Numbers

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Published: 2022-08-30

Page: 553-560

Monica U. Feliksiak * Language School Cracov Poland.

*Author to whom correspondence should be addressed.


We derive two asymptotic formulae for the upper bound on the sum of the first n primes. Both the Supremum and the Estimate of the sum are superior to known bounds. The Estimate bound had been derived to promote effciency of estimation of the sum.

Keywords: R. Mandl's inequality, sum of primes Supremum, sum of primes estimate

How to Cite

Feliksiak, M. U. (2022). An Improved Bound on the Sum of Prime Numbers. Asian Journal of Pure and Applied Mathematics, 4(1), 553–560. Retrieved from


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Axler, Christian. On a Sequence involving Prime Numbers. Journal of Integer Sequences; 2015.

Axler, Christian. New bounds for the sum of the rst n prime numbers. preprint:

arXiv:1606.06874 [math.NT]; 2016.

Rosser JB and Schoenfeld L. Sharper bounds for the Chebyshev functions θx and ψx.

Mathematics of Computation. 1975; 29(129): 243-269.

Dusart P. Autour de la fonction qui compte le nombre de nombres premiers; 1998.

Hassani M. A renement of Mandl's inequality and approximation of the product p1p2 pn.

preprint: arXiv:math/0606765v1[math.NT]; 2006.

Feliksiak J. The elementary proof of the Riemann's hypothesis; 2020.


Crandall R and Pomerance C. Prime numbers, a computational perspective. Springer Verlag,

New York; 2005.

Erdos P. On the dierence of consecutive primes. The Quarterly Journal of Mathematics.


Erdos P, Straus EG. Remarks on the dierences between consecutive primes. Elem. Math.


Hardy GH, and Wright EM. An introduction to the theory of numbers. Oxford University

Press, London; 1968.

Panaitopol L. An inequality concerning prime numbers. NNTDM; 1999.

Ruiz SM. 81.27 A result on prime numbers. The Mathematical Gazette. 1997;81(491):269-70.

Shanks D. On maximal gaps between successive primes. Mathematics of Computation.