论文信息 - A prime sum involving Bernoulli numbers

A prime sum involving Bernoulli numbers

In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.

J. Pain

[1] K. Atanassov. Formulas for the n-th prime number , 2021, Notes on Number Theory and Discrete Mathematics.

[2] Dimitar G. Dimitrov,et al. On the software computation of the formulae for the n-th prime number , 2019, Notes on Number Theory and Discrete Mathematics.

[3] Manuel Eberl,et al. Bernoulli Numbers , 2017, Arch. Formal Proofs.

[4] S. Ruiz. A new formula for the nth prime , 2004, math/0406001.

[5] T. K. Atanassov. A New Formula for the n-th Prime Number , 2001 .

[6] Wieb Bosma,et al. Algorithmic Number Theory , 2000, Lecture Notes in Computer Science.

[7] H. K. Krishnapriyan. Eulerian Polynomials and Faulhaber's Result on Sums of Powers of Integers , 1995 .

[8] B. Berndt. Ramanujan’s Theory of Prime Numbers , 1994 .

[9] Paulo Ribenboim,et al. The little book of big primes , 1991 .

[10] S. Golomb. Formulas for the next prime , 1976 .

[11] S. Golomb. A Direct Interpretation of Gandhi's Formula , 1974 .

[12] C. V. Eynden. A Proof of Gandhi's Formula for the nth Prime , 1972 .

[13] K. Namboodiripad. A note on formulae for the n th prime , 1971 .

[14] Ralph G. Archibald,et al. An introduction to the theory of numbers , 1970 .

[15] E. T.. An Introduction to the Theory of Numbers , 1946, Nature.

[16] Franz Mertens,et al. Ein Beitrag zur analytischen Zahlentheorie. , 1874 .