Relevant bibliographies by topics / Prime factorization

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Prime factorization'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Prime factorization"

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KNOPFMACHER, ARNOLD, and FLORIAN LUCA. "ON PRIME-PERFECT NUMBERS." International Journal of Number Theory 07, no. 07 (2011): 1705–16. http://dx.doi.org/10.1142/s1793042111004447.

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We prove that the Diophantine equation [Formula: see text] has only finitely many positive integer solutions k, p1, …, pk, r1, …, rk, where p1, …, pk are distinct primes. If a positive integer n has prime factorization [Formula: see text], then [Formula: see text] represents the number of ordered factorizations of n into prime parts. Hence, solutions to the above Diophantine equation are designated as prime-perfect numbers.
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Liu, Jinwang, Tao Wu, Dongmei Li, and Jiancheng Guan. "On Zero Left Prime Factorizations for Matrices over Unique Factorization Domains." Mathematical Problems in Engineering 2020 (April 22, 2020): 1–3. http://dx.doi.org/10.1155/2020/1684893.

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In this paper, zero prime factorizations for matrices over a unique factorization domain are studied. We prove that zero prime factorizations for a class of matrices exist. Also, we give an algorithm to directly compute zero left prime factorizations for this class of matrices.
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Papadakis, Ioannis N. M. "Algebraic Representation of Primes by Hybrid Factorization." Mathematics and Computer Science 9, no. 1 (2024): 12–25. http://dx.doi.org/10.11648/j.mcs.20240901.12.

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The representation of integers by prime factorization, proved by Euclid in the Fundamental Theorem of Arithmetic −also referred to as the Prime Factorization Theorem− although universal in scope, does not provide insight into the algebraic structure of primes themselves. No such insight is gained by summative prime factorization either, where a number can be represented as a sum of up to three primes, assuming Goldbach’s conjecture is true. In this paper, a third type of factorization is introduced, called hybrid prime factorization, defined as the representation of a number as sum −or differe
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Mahato, Prabhat, and Aayush Shah. "A Review of Prime Numbers, Squaring Prime Pattern, Different Types of Primes and Prime Factorization Analysis." International Journal for Research in Applied Science and Engineering Technology 11, no. 7 (2023): 2036–43. http://dx.doi.org/10.22214/ijraset.2023.54904.

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Abstract: The study of prime numbers and their properties has always been an intriguing and fascinating topic for mathematicians. Primes can be considered the “basic building blocks,” the atoms, of the natural numbers. They play a significant role in number theory. Also, prime numbers, in this current world of computers and digitalization, have paramount significance for the computer programmers and scientists to tackle relevant real-life problems. Since long time, many studies and researches have been conducted regarding prime numbers pattern. In this paper, a squaring prime pattern is presen
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MANN, A., M. REVZEN, and J. ZAK. "THE PHYSICS OF FACTORIZATION." International Journal of Quantum Information 04, no. 01 (2006): 173–80. http://dx.doi.org/10.1142/s0219749906001670.

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The Ndistinct prime numbers that make up a composite number M allow its bi-partitioning into pairs of two relatively prime factors. Each such pair defines a pair of conjugate representations. An example of such pairs of conjugate representations, each of which spans the M-dimensional space, are the kq representations, which are the most natural representations for periodic systems. Here, we emphasize their relevance to factorizations: the number of prime numbers that make up M relates directly to the number of conjugate pairs of kq representations. It is also shown how Schwinger's factorizatio
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MEYEROVITCH, TOM. "Direct topological factorization for topological flows." Ergodic Theory and Dynamical Systems 37, no. 3 (2015): 837–58. http://dx.doi.org/10.1017/etds.2015.67.

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This paper considers the general question of when a topological action of a countable group can be factored into a direct product of non-trivial actions. In the early 1980s, D. Lind considered such questions for $\mathbb{Z}$-shifts of finite type. In particular, we study direct factorizations of subshifts of finite type over $\mathbb{Z}^{d}$ and other groups, and $\mathbb{Z}$-subshifts which are not of finite type. The main results concern direct factors of the multidimensional full $n$-shift, the multidimensional $3$-colored chessboard and the Dyck shift over a prime alphabet. A direct factor
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WOLF, Marc, and François WOLF. "On the Factorization of Numbers of the Form X^2+c." Transactions on Machine Learning and Artificial Intelligence 10, no. 4 (2022): 59–77. http://dx.doi.org/10.14738/tmlai.104.12959.

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We study the factorization of the numbers N=X^2+c, where c is a fixed constant, and this independently of the value of gcd⁡(X,c). We prove the existence of a family of sequences with arithmetic difference (Un,Zn) generating factorizations, i.e. such that: (Un)^2+c= ZnZn+1. The different properties demonstrated allow us to establish new factorization methods by a subset of prime numbers and to define a prime sieve. An algorithm is presented on this basis and leads to empirical results which suggest a positive answer to Landau's 4th problem.
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Marchei, Daniele, and Emanuela Merelli. "RNA secondary structure factorization in prime tangles." BMC Bioinformatics 23, S6 (2022): 345. https://doi.org/10.1186/s12859-022-04879-5.

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<strong>Background: </strong>Due to its key role in various biological processes, RNA secondary structures have always been the focus of in-depth analyses, with great efforts from mathematicians and biologists, to find a suitable abstract representation for modelling its functional and structural properties. One contribution is due to Kauffman and Magarshak, who modelled RNA secondary structures as mathematical objects <i>constructed</i> in link theory: <i>tangles of the Brauer Monoid</i>. In this paper, we extend the tangle-based model with its minimal prime factorization, useful to analyze p
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Rengkung, Matthew Evans Audric, and Arya Wicaksana. "RSA Prime Factorization on IBM Qiskit." Journal of Internet Services and Information Security 13, no. 2 (2023): 203–10. http://dx.doi.org/10.58346/jisis.2023.i2.013.

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The advancement of quantum computing in recent years poses severe threats to the RSA public-key cryptosystem. The RSA cryptosystem fundamentally relies its security on the computational hardness of number theory problems: prime factorization (integer factoring). Shor’s quantum factoring algorithm could theoretically answer the computational problem in polynomial time. This paper contributes to the experiment and demonstration of Shor’s quantum factoring algorithm for RSA prime factorization using IBM Qiskit. The performance of the quantum program is evaluated based on user time and the success
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Overmars, Anthony, and Sitalakshmi Venkatraman. "New Semi-Prime Factorization and Application in Large RSA Key Attacks." Journal of Cybersecurity and Privacy 1, no. 4 (2021): 660–74. http://dx.doi.org/10.3390/jcp1040033.

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Semi-prime factorization is an increasingly important number theoretic problem, since it is computationally intractable. Further, this property has been applied in public-key cryptography, such as the Rivest–Shamir–Adleman (RSA) encryption systems for secure digital communications. Hence, alternate approaches to solve the semi-prime factorization problem are proposed. Recently, Pythagorean tuples to factor semi-primes have been explored to consider Fermat’s Christmas theorem, with the two squares having opposite parity. This paper is motivated by the property that the integer separating these
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Dissertations / Theses on the topic "Prime factorization"

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Eppens, Daniel. "Prime Factorization by Quantum Adiabatic Computation." Thesis, KTH, Fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-138164.

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Bollinger, Patrick James. "Prime Factorization Through Reversible Logic Gates." Youngstown State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1558867948427409.

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Jacobsson, Mattias. "Bitwise relations between n and φ(n) : A novel approach at prime number factorization". Thesis, Blekinge Tekniska Högskola, Institutionen för datalogi och datorsystemteknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-16655.

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Cryptography plays a crucial role in today’s society. Given the influence, cryptographic algorithms need to be trustworthy. Cryptographic algorithms such as RSA relies on the problem of prime number factorization to provide its confidentiality. Hence finding a way to make it computationally feasible to find the prime factors of any integer would break RSA’s confidentiality. The approach presented in this thesis explores the possibility of trying to construct φ(n) from n. This enables factorization of n into its two prime numbers p and q through the method presented in the original RSA paper. T
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Wilson, Keith Eirik. "Factoring Semiprimes Using PG2N Prime Graph Multiagent Search." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/219.

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In this thesis a heuristic method for factoring semiprimes by multiagent depth-limited search of PG2N graphs is presented. An analysis of PG2N graph connectivity is used to generate heuristics for multiagent search. Further analysis is presented including the requirements on choosing prime numbers to generate 'hard' semiprimes; the lack of connectivity in PG1N graphs; the counts of spanning trees in PG2N graphs; the upper bound of a PG2N graph diameter and a conjecture on the frequency distribution of prime numbers on Hamming distance. We further demonstrated the feasibility of the HD2 breadth
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Puffenberger, Owen. "Uniqueness of Bipartite Factors in Prime Factorizations Over the Direct Product of Graphs." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3017.

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While it has been known for some time that connected non-bipartite graphs have unique prime factorizations over the direct product, the same cannot be said of bipartite graphs. This is somewhat vexing, as bipartite graphs do have unique prime factorizations over other graph products (the Cartesian product, for example). However, it is fairly easy to show that a connected bipartite graph has only one prime bipartite factor, which begs the question: is such a prime bipartite factor unique? In other words, although a connected bipartite graph may have multiple prime factorizations over the direct
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Rezola, Nolberto. "Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/205.

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The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This
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Borg, Caroline W., and Erik Dackebro. "A Comparison of Performance Between a CPU and a GPU on Prime Factorization Using Eratosthene's Sieve and Trial Division." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-208678.

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There has been remarkable advancement in Multi-cored Processing Units over the past decade. GPUs, which were originally designed as a specialized graphics processor, are today used in a wide variety of other areas. Their ability to solve parallel problems is unmatched due to their massive amount of simultaneously running cores. Despite this, most algorithms in use today are still fully sequential and do not utilize the processing power available. The Sieve of Eratosthenes and Trial Division are two very naive algorithms which combined can be used to find a number's unique combinataion of prime
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Hedenström, Felix. "Trial Division : Improvements and Implementations." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-211090.

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Trial division is possibly the simplest algorithm for factoring numbers.The problem with Trial division is that it is slow and wastes computationaltime on unnecessary tests of division. How can this simple algorithms besped up while still being serial? How does this algorithm behave whenparallelized? Can a superior serial and a parallel version be combined intoan even more powerful algorithm?To answer these questions the basics of trial divisions where researchedand improvements where suggested. These improvements where later im-plemented and tested by measuring the time it took to factorize a
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Kišac, Matej. "Distribuované aplikace s využitím frameworku Windows Communication Foundation." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242060.

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This thesis deals with distributed applications and WCF framework. The first part is based on theoretical information about distributed systems and we also concentrate on models of distributed systems. Next part describes WCF framework and key elements of WCF application. The following chapter is designated to introduce information about prime factorization. Then the knowledge from previous parts is used to create examples of service-oriented applications. In conclusion we discuss main parts of designing distributed application to solve factorization problem. Finally the comparison of distribu
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Johansson, Angela. "Distributed System for Factorisation of Large Numbers." Thesis, Linköping University, Department of Electrical Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1883.

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<p>This thesis aims at implementing methods for factorisation of large numbers. Seeing that there is no deterministic algorithm for finding the prime factors of a given number, the task proves rather difficult. Luckily, there have been developed some effective probabilistic methods since the invention of the computer so that it is now possible to factor numbers having about 200 decimal digits. This however consumes a large amount of resources and therefore, virtually all new factorisations are achieved using the combined power of many computers in a distributed system. </p><p>The nature of the
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Books on the topic "Prime factorization"

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Bressoud, David M. Factorization and primality testing. Springer-Verlag, 1989.

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Riesel, Hans. Prime numbers and computer methods for factorization. 2nd ed. Birkhäuser, 1994.

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Riesel, Hans. Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8298-9.

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Riesel, Hans. Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1089-2.

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Riesel, Hans. Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0251-6.

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Riesel, Hans. Prime numbers and computer methods for factorization. Birkhäser, 2012.

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Fernández-Asenjo, Félix López. Introducción a la teoría de números primos: Aspectos algebraicos y analíticos. Instituto de Ciencias de la Educación, Universidad de Valladolid, 1990.

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Lappan, Glenda. Prime time: Factors and multiples. Dale Seymour Publications, 1998.

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Glenda, Lappan, and Michigan State University, eds. Prime time: Factors and multiples. Dale Seymour Publications, 1998.

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Glenda, Lappan, and Michigan State University, eds. Prime time: Factors and multiples. Dale Seymour Publications, 1996.

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Book chapters on the topic "Prime factorization"

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Riesel, Hans. "Factorization." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1089-2_5.

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Effinger, Gove, and Gary L. Mullen. "Prime Numbers and Factorization." In Elementary Number Theory. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003193111-2.

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Riesel, Hans. "Modern Factorization Methods." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0251-6_6.

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Riesel, Hans. "Modern Factorization Methods." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8298-9_6.

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Riesel, Hans. "Prime Numbers and Cryptography." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0251-6_7.

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Riesel, Hans. "Prime Numbers and Cryptography." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8298-9_7.

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Riesel, Hans. "Prime Numbers and Cryptography." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1089-2_6.

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Riesel, Hans. "Classical Methods of Factorization." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0251-6_5.

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Riesel, Hans. "Classical Methods of Factorization." In Prime Numbers and Computer Methods for Factorization. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8298-9_5.

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Balasubramaniam, P., P. Muthukumar, and Wan Ainun Binti Mior Othman. "Prime Factorization without Using Any Approximations." In Mathematical Modelling and Scientific Computation. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28926-2_61.

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Conference papers on the topic "Prime factorization"

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Yang, Jiale, Yarong Wu, Guhao Zhao, Zhifang Chen, Zhichong Zhou, and Chuanlong Zhang. "Conflict detection and resolution for unmanned aerial vehicles (UAVs) based on prime factorization." In Eighth International Conference on Traffic Engineering and Transportation System (ICTETS 2024), edited by Xiantao Xiao and Jia Yao. SPIE, 2024. https://doi.org/10.1117/12.3054500.

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Dass, Pranav, Harish Sharma, Jagdish Chand Bansal, and Kendall E. Nygard. "Meta heuristics for prime factorization problem." In 2013 World Congress on Nature and Biologically Inspired Computing (NaBIC). IEEE, 2013. http://dx.doi.org/10.1109/nabic.2013.6617850.

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McGeer, P. C., and R. K. Brayton. "Efficient prime factorization of logic expressions." In the 1989 26th ACM/IEEE conference. ACM Press, 1989. http://dx.doi.org/10.1145/74382.74420.

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Sharp, Tristan A., Rishabh Khare, Erick Pederson, and Fabio L. Traversa. "A Memcomputing Approach to Prime Factorization." In 2023 IEEE International Conference on Rebooting Computing (ICRC). IEEE, 2023. http://dx.doi.org/10.1109/icrc60800.2023.10386235.

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Huang, Lican. "New Prime Factorization Algorithm and Its Parallel Computing Strategy." In 2015 1st International Conference on Information Technologies in Education and Learning (ICMII 2015). Atlantis Press, 2016. http://dx.doi.org/10.2991/icitel-15.2016.27.

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Rutkowski, Emilia, and Sheridan Houghten. "Cryptanalysis of RSA: Integer Prime Factorization Using Genetic Algorithms." In 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2020. http://dx.doi.org/10.1109/cec48606.2020.9185728.

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Mishra, Mohit, Utkarsh Chaturvedi, and Saibal K. Pal. "A Multithreaded Bound Varying Chaotic Firefly Algorithm for prime factorization." In 2014 IEEE International Advance Computing Conference (IACC). IEEE, 2014. http://dx.doi.org/10.1109/iadcc.2014.6779518.

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Mihalák, Matúš, Przemysław Uznański, and Pencho Yordanov. "Prime Factorization of the Kirchhoff Polynomial: Compact Enumeration of Arborescences." In 2016 Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974324.10.

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Bollinger, Patrick J., Frank X. Li, and Eric W. MacDonald. "A Novel Encryption Methodology with Prime Factorization through Reversible Logic Gates." In NAECON 2019 - IEEE National Aerospace and Electronics Conference. IEEE, 2019. http://dx.doi.org/10.1109/naecon46414.2019.9057958.

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Liu, Jianquan, Shoji Nishimura, and Takuya Araki. "P-Index: A Novel Index Based on Prime Factorization for Similarity Search." In 2019 IEEE International Conference on Big Data and Smart Computing (BigComp). IEEE, 2019. http://dx.doi.org/10.1109/bigcomp.2019.8679353.

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