论文链接：https://pan.quark.cn/s/fbffb412bf40
https://pan.baidu.com/s/1QyCDYebTr7_HB-1pFGm40Q?pwd=1111
原创探索论文
- 主要论文可见预印版TechRxiv: https://www.techrxiv.org/authors/Wei_Ren/8333871
Notes on elementary proof of Graham conjecture
- 刊物：JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY
- 作者：Wei Ren
- 链接：https://doi.org/10.1080/09720529.2021.1995221
- doi: 10.1080/09720529.2021.1995221
- PDF下载：https://wwsc.lanzouo.com/imBF01l8ovpg
Collatz Dynamics is Partitioned by Residue Class Regularly, Research in Mathematics
- 刊物：Research in Mathematics, Taylor & Francis,
- 作者：Wei Ren
- 分区：CCF C
- 链接：https://www.tandfonline.com/doi/full/10.1080/27684830.2023.2269657
- doi: 10.1080/27684830.2023.2269657
- PDF下载：https://wwsc.lanzouy.com/i57HR1cbmujg
A Symmetric Uniform Formula and Sole Index Method for Sieving (Twin) Primes
- 刊物：2020 IEEE 19th International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom20)
- 作者：Wei Ren*（通信作者）
- 分区：CCF C
- 链接：https://doi.ieeecomputersociety.org/10.1109/TrustCom50675.2020.00220
- doi：10.1109/TrustCom50675.2020.00220
- PDF下载：https://wwsc.lanzouy.com/iodtN190xukj
A New Approach on Proving Collatz Conjecture
- 刊物：Journal of Mathematics, Hindawi, Jan. 2019, ID 6129836
- 作者：Wei Ren*
- 链接：https://www.hindawi.com/journals/jmath/2019/6129836/
- doi：10.1155/2019/6129836
- 简介：该论文给出了一个证明Collatz猜想的一种新途径，即将证明规约到证明精简Collatz猜想（Reduced Collatz Conjecture）。并指出，通过计算精简Collatz动态（Reduced Collatz Dynamics）并分析该动态的属性，来进一步证明精简Collatz猜想。论文被牛津大学的论文所引用。
- PDF下载：https://wwsc.lanzouy.com/idSOh190xudc
A Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of over the Count of Is Larger than ln3/ln2
- 刊物： International Journal of Mathematics and Mathematical Sciences
- 作者：Wei Ren*（通信作者）
- 链接：https://www.techrxiv.org/ndownloader/files/21196578
- doi：10.1155/2020/5946759
- PDF下载：https://wwsc.lanzouy.com/iux3W190xuhg
Ratio and Partition are Revealed in Proposed Graph on Reduced Collatz Dynamics
- 刊物： Proc. Of 2019 IEEE Intl Conf on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA/BDCloud/SocialCom/SustainCom) , pp.474-483, 16-18 Dec. 2019, Xiamen, China
- 作者：Wei Ren*
- 分区：CCF C
- 链接：https://ieeexplore.ieee.org/document/9047265
- doi：10.1109/ISPA-BDCloud-SustainCom-SocialCom48970.2019.00076
- 简介：该论文提出一种树形图，该图直观地揭示了精简Collatz动态计算过程的3个基本属性，比如ratio的界，partition属性（即可分成不相交子集的并）。
- PDF下载：https://wwsc.lanzouy.com/i3Eou190xt5i
Reduced Collatz dynamics data reveals properties for the future proof of Collatz conjecture
- 刊物： Data, MDPI, Data 2019, 4, 89
- 作者：Wei Ren*
- 链接：https://www.mdpi.com/2306-5729/4/2/89/pdf
- doi：10.3390/data4020089
- 简介：该论文是一篇科学数据论文。论文给出了计算精简Collatz动态以及验证精简Collatz猜想所需要的主要算法，以及这些算法所产生的数据，算法的代码和数据均可以通过开放数据库下载。该论文也归纳总结并列出了我们上传到IEEE Dataport上的数据集和代码。
- PDF下载：https://wwsc.lanzouy.com/is2Nn190xtad
A Symmetric Uniform Formula and Sole Index Method for Sieving (Twin) Primes
- 刊物： Proc. Of The 19th IEEE International Conference on Trust, Security and Privacy in Computing and Communications (IEEE TrustCom 2020), Guangzhou, China, December 29, 2020 - January 1, 2021
- 作者：Wei Ren
- 分区：CCF C
- 链接：https://ieeexplore.ieee.org/document/9343217
- doi：10.1109/TrustCom50675.2020.00220
- PDF下载：https://wwsc.lanzouy.com/iodtN190xukj
Collatz Conjecture for 2^100000-1 is True - Algorithms for Verifying Extremely Large Numbers
- 刊物：2018 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI), Guangzhou, China, 2018, pp. 411-416
- 作者：Wei Ren*（通信作者）, Simin Li, Ruiyang Xiao, Wei Bi
- 分区：CCF C
- 链接：https://ieeexplore.ieee.org/document/8560077
- doi： doi: 10.1109/SmartWorld.2018.00099
- 简介：该论文给出了如何计算超大整数（例如长度为10万bit的整数）的Collatz动态（回到1的计算过程）的关键算法，即可以将数值计算转变为逻辑计算该算法可以利用外部存储计算无限长度的整数bit串通过3x+1或者x/2回到1的过程，而与计算机器的内存限制无关。
- PDF下载：https://wwsc.lanzouy.com/iXlmK190xr9a
Reduced Collatz Dynamics is Periodical and the Period Equals 2 to the Power of the Count of x/2
- 刊物：Research in Mathematical Science, Springer
- 作者：Wei Ren
- 链接：https://www.techrxiv.org/ndownloader/files/21196512
- doi：Doi: 10.36227/techrxiv.11664501.v1
- 简介：该论文严格证明了精简Collatz动态的周期性，并证明其周期等于2的一个幂次，指数是精简Collatz动态中x/2计算的次数。
- PDF下载：https://wwsc.lanzouy.com/ikOx3190xtdg
Collatz Dynamics is Partitioned by Residue Class Regularly
- 刊物：Research in Mathematical Science, Springer
- 作者：Wei Ren
- 链接：https://www.techrxiv.org/ndownloader/files/21377280
- Doi: 10.36227/techrxiv.11742669.v1
- 简介：该论文严格证明了Collatz动态（可Partition，分片，即分割成不相交的子集的并集），与剩余类之间的关系。
- PDF下载：https://wwsc.lanzouy.com/ih0zt190xrcd
Notes on Elementary Proof of Graham Conjecture
- 刊物：Journal of Discrete Mathematical Sciences & Cryptography, Taylor-Francis, Accepted.
- 作者：Wei Ren
- 链接：http://dx.chinadoi.cn/10.1080/09720529.2021.1995221
- doi：https://doi.org/10.1080/09720529.2021.1995221
- 下载链接：
Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of (x/2) over the Count of 3*x + 1 Is Larger than ln3/ln2
- 刊物：International Journal of Mathematics and Mathematical Sciences, Hindawi, Volume2020, Article ID 5946759
- 作者：Wei Ren
- 链接：https://doi.org/10.1155/2020/5946759
- doi: https://doi.org/10.36227/techrxiv.11664567.v1
- 简介：该论文严格证明了精简Collatz动态中的x/2与3*x+1次数间的比例关系的下界是ln3/ln2。
- PDF下载：<https://www.techrxiv.org/ndownloader/files/21196578>
How to Fast Verify Collatz Conjecture by Automata
- 刊物：Proc. Of 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC/SmartCity/DSS), pp. 2720-2729, 10-12 Aug. 2019, Zhangjiajie, China
- 作者：Wei Ren, Ruiyang Xiao
- 分区：CCF C
- 链接：How to Fast Verify Collatz Conjecture by Automata - Scilit
- Doi: 10.1109/HPCC/SmartCity/DSS.2019.00382
- 简介：该论文推导了一些快速计算的公式，并给出了利用自动机快速验证Colltaz猜想的算法。
- PDF下载：https://wwsc.lanzouy.com/i4cL5190xrvc
Notes on Elementary Proof of Graham Conjecture
- 刊物：Journal of Discrete Mathematical Sciences & Cryptography, Taylor & Francis
- 作者：Wei Ren
- 链接：https://www.tandfonline.com/doi/abs/10.1080/09720529.2021.1995221
- doi：https://doi.org/10.1080/09720529.2021.1995221
- PDF下载：
Reduced Collatz Dynamics is Periodical and the Period Equals 2 to the Power of the Count of x/2
- 作者：Wei Ren
- 链接：https://doi.org/10.48550/arXiv.2304.10491
- doi：https://doi.org/10.48550/arXiv.2304.10491
- 简介：发现Collatz动态的周期性并给出周期的计算方法
- PDF下载：https://wwsc.lanzouy.com/ikOx3190xtdg
Collatz Dynamics is Partitioned by Residue Class Regularly
- 作者：Wei Ren
- 链接：https://doi.org/10.48550/arXiv.2304.11388
- doi：10.48550/arXiv.2304.11388
- 简介：关于Collatz动态与剩余类之间的关系，发现Collatz动态可根据剩余类构成严格分划
- PDF下载：https://wwsc.lanzouy.com/ih0zt190xrcd
Reduced Collatz Dynamics for Integers from 3 to 999999,
作者：Wei Ren
doi：10.48550/arXiv.2304.11388
简介：关于Collatz动态与剩余类之间的关系，发现Collatz动态可根据剩余类构成严格分划
Exploring properties in reduced Collatz dynamics,
https://ieee-dataport.org/documents/exploring-properties-reduced-collatz-dynamics
Collatz Automata and Compute Residue Class from Reduced Dynamics by Formula,
Exploring the ratio between the count of x/2 and the count of (3*x+1)/2 in original dynamics for extremely large starting integers asymptotically,
Exploring the inverse mapping from a dynamics to a residue class - inputting a reduced dynamics or partial dynamics and outputting a residue class,
A PRIME SIEVE METHOD,
https://ieee-dataport.org/documents/prime-sieve-method
主要C程序源代码和输出结果数据可见公开上传的数据库
- IEEE Dataport: https://ieee-dataport.org/authors/wei-ren
