Paper 2013/843
A Study of Goldbach's conjecture and Polignac's conjecture equivalence issues
Jian Ye and Chenglian Liu
Abstract
The famous Goldbach's conjecture and Polignac's conjecture are two of all unsolved problems in the field of number theory today. As well known, the Goldbach's conjecture and the Polignac's conjecture are equivalent. Most of the literatures does not introduce about internal equivalence in Polignac's conjecture. In this paper, we would like to discuss the internal equivalence to the Polignac's conjecture, say $T_{2k}(x)$ and $T(x)$ are equivalent. Since $T_{2k}\sim T(x)\sim 2c\cdot \frac{x}{(\ln x)^{2}}$, we rewrite and reexpress to $T(x)\sim T_{4}(x)\sim T_{8}(x)\sim T_{16}(x)\sim T_{32}(x)\sim T_{2^{n}}(x)\sim 2c\cdot \frac{x}{(\ln x)^{2}}$. And then connected with the Goldbach's conjecture. Finally, we will point out the important prime number symmetry role of play in these two conjectures.
Metadata
 Available format(s)
 Publication info
 Preprint.
 Keywords
 Goldbach's conjecturePolignac's conjectureEquivalent
 Contact author(s)
 chenglian liu @ gmail com
 History
 20131220: last of 3 revisions
 20131217: received
 See all versions
 Short URL
 https://ia.cr/2013/843
 License

CC BY
BibTeX
@misc{cryptoeprint:2013/843, author = {Jian Ye and Chenglian Liu}, title = {A Study of Goldbach's conjecture and Polignac's conjecture equivalence issues}, howpublished = {Cryptology ePrint Archive, Paper 2013/843}, year = {2013}, note = {\url{https://eprint.iacr.org/2013/843}}, url = {https://eprint.iacr.org/2013/843} }