Mladen Vassilev-Missana

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 19, 2013, Number 2, Pages 43—48

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## Details

### Authors and affiliations

Mladen Vassilev-Missana

*5 V. Hugo Str., 1124 Sofia, Bulgaria*

### Abstract

In the paper for any integer n ≥ 5 the validity of the formula

(where π_{2} denotes the twin prime counting function and φ is Euler’s totient function) is established. Also for any integer n ≥ 5 the formula

(where f is arbitrary artihmetic function with strictly positive values satisfying the condition

is proved.

### Keywords

- Prime number (prime)
- Twin primes
- Twin prime counting function
- Arithmetic function

### AMS Classification

- 11A25
- 11A41

### References

- Ribenboim, P. The New Book of Prime Number Records (3rd Edition), Springer-Verlag, New York, 1996.
- Vassilev-Missana, M. Some new formulae for the twin prime counting function
*π*_{2}, Notes on Number Theory and Discrete Mathematics, Vol 7, 2001, No. 1, 10–14.

## Related papers

## Cite this paper

APAVassilev-Missana, M. (2013). Note on some explicit formulae for twin prime counting function. Notes on Number Theory and Discrete Mathematics, 19(2), 43-48.

ChicagoVassilev-Missana, Mladen. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 43-48.

MLAVassilev-Missana, Mladen. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 43-48. Print.