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Relevant bibliographies by topics / Numbers, Prime. Factorization (Mathematics)

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Academic literature on the topic 'Numbers, Prime. Factorization (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "Numbers, Prime. Factorization (Mathematics)"

1

Wagstaff, S. S., and Hans Riesel. "Prime Numbers and Computer Methods for Factorization." Mathematics of Computation 48, no. 177 (1987): 439. http://dx.doi.org/10.2307/2007903.

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Feldman, Ziv, and Matt B. Roscoe. "Encouraging Teachers to Make Use of Multiplicative Structure." Mathematics Teacher Educator 7, no. 1 (2018): 60–85. http://dx.doi.org/10.5951/mathteaceduc.7.1.0060.

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The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to identify its factors, and presents evidence of the impact of the intervention. Results point toward improved abilities to use a number's prime factorization to sort factors and nonfactors across four factor subtypes, to create factor lists, and to construc

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Pomerance, Carl. "Book Review: Prime numbers and computer methods for factorization." Bulletin of the American Mathematical Society 18, no. 1 (1988): 61–66. http://dx.doi.org/10.1090/s0273-0979-1988-15599-1.

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Fachrurazi, Fachrurazi. "PEMBELAJARAN MATEMATIKA REALISTIK DI SEKOLAH DASAR PADA MATERI FPB DAN KPK DENGAN MODEL PENYAJIAN PAKET MAKANAN." Al Khawarizmi: Jurnal Pendidikan dan Pembelajaran Matematika 1, no. 2 (2017): 113. http://dx.doi.org/10.22373/jppm.v1i2.3425.

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So far, the concept of the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two numbers are still being taught procedurally whether it is seeking multiples or by understanding prime numbers and prime factorization. This way often makes the students difficulties in determining the GCD and LCM. To overcome such things, the authors will offer a solution in learning mathematics material GCD and LCM in elementary school taught with Approach Realistic Mathematics Education (RME) food package presentation model. Mathematical learning with this approach is believed to make students

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Wagstaff, S. S., and Hideo Wada. "Computers and Prime Factorization." Mathematics of Computation 53, no. 187 (1989): 451. http://dx.doi.org/10.2307/2008382.

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Zazkis, Rina, and Stephen Campbell. "Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding." Journal for Research in Mathematics Education 27, no. 5 (1996): 540–63. http://dx.doi.org/10.5951/jresematheduc.27.5.0540.

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This study contributes to a growing body of research on teachers' content knowledge in mathematics. The domain under investigation was elementary number theory. Our main focus concerned the concept of divisibility and its relation to division, multiplication, prime and composite numbers, factorization, divisibility rules, and prime decomposition. We used a constructivist-oriented theoretical framework for analyzing and interpreting data acquired in clinical interviews with preservice teachers. Participants' responses to questions and tasks indicated pervasive dispositions toward procedural att

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Davis, Simon. "A rationality condition for the existence of odd perfect numbers." International Journal of Mathematics and Mathematical Sciences 2003, no. 20 (2003): 1261–93. http://dx.doi.org/10.1155/s0161171203108277.

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A rationality condition for the existence of odd perfect numbers is used to derive an upper bound for the density of odd integers such thatσ(N)could be equal to2N, whereNbelongs to a fixed interval with a lower limit greater than10300. The rationality of the square root expression consisting of a product of repunits multiplied by twice the base of one of the repunits depends on the characteristics of the prime divisors, and it is shown that the arithmetic primitive factors of the repunits with different prime bases can be equal only when the exponents are different, with possible exceptions de

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Corso, Ilaria Del. "Factorization of Prime Ideal Extensions in Number Rings." Mathematics of Computation 58, no. 198 (1992): 849. http://dx.doi.org/10.2307/2153222.

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Del Corso, Ilaria. "Factorization of prime ideal extensions in number rings." Mathematics of Computation 58, no. 198 (1992): 849. http://dx.doi.org/10.1090/s0025-5718-1992-1122062-2.

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Tekir, Ünsal. "A Note on Dedekind and ZPI Modules." Algebra Colloquium 13, no. 01 (2006): 41–45. http://dx.doi.org/10.1142/s1005386706000071.

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Let R be a domain. A non-zero R-module M is called a Dedekind module if every submodule N of M such that N ≠ M either is prime or has a prime factorization N=P1P2… PnN*, where P1, P2, … Pn are prime ideals of R and N* is a prime submodule in M. When R is a ring, a non-zero R-module M is called a ZPI module if every submodule N of M such that N ≠ M either is prime or has a prime factorization. The purpose of this paper is to introduce interesting and useful properties of Dedekind and ZPI modules.

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Dissertations / Theses on the topic "Numbers, Prime. Factorization (Mathematics)"

1

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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2

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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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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Shiu, Daniel Kai Lun. "Prime numbers in arithmetic progressions." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318815.

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Wolczuk, Dan. "Intervals with few Prime Numbers." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1064.

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In this thesis we discuss some of the tools used in the study of the number of primes in short intervals. In particular, we discuss a large sieve density estimate due to Gallagher and two classical delay equations. We also show how these tools have been used by Maier and Stewart and provide computational data to their result.

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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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Haugland, Jan Kristian. "Application of sieve methods to prime numbers." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300131.

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Kolenick, Joseph F. "On exponentially perfect numbers relatively prime to 15 /." Connect to resource online, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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Kolenick, Joseph F. Jr. "On Exponentially Perfect Numbers Relatively Prime to 15." Youngstown State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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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 "Numbers, Prime. Factorization (Mathematics)"

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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. Birkhäser, 2012.

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

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Prime numbers and computer methods for factorization. Birkhäuser, 1985.

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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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Primes and programming: An introduction to number theory with computing. Cambridge University Press, 1993.

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Giblin, P. J. Primes and programming: An introduction to number theory with computing. Cambridge University Press, 1992.

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Analytic methods in the analysis and design of number-theoretic algorithms. MIT Press, 1985.

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9

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

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10

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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Book chapters on the topic "Numbers, Prime. Factorization (Mathematics)"

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Gallier, Jean. "Partial Orders, Lattices, Well-Founded Orderings, Unique Prime Factorization in ℤ and GCDs, Equivalence Relations, Fibonacci and Lucas Numbers, Public Key Cryptography and RSA, Distributive Lattices, Boolean Algebras, Heyting Algebras." In Discrete Mathematics. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-8047-2_5.

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2

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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Rivat, Joël. "Prime Numbers." In Lecture Notes in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74908-2_1.

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4

Stein, William. "Prime Numbers." In Undergraduate Texts in Mathematics. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-85525-7_1.

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Jones, Gareth A., and J. Mary Jones. "Prime Numbers." In Springer Undergraduate Mathematics Series. Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-0613-5_2.

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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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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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9

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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Zazkis, Rina, Nathalie Sinclair, and Peter Liljedahl. "On Prime Numbers." In Lesson Play in Mathematics Education:. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3549-5_6.

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Conference papers on the topic "Numbers, Prime. Factorization (Mathematics)"

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Kristyan, Sandor. "On the statistical distribution of prime numbers: A view from where the distribution of prime numbers are not erratic." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992696.

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Hermawan, Nanang Triagung Edi, Edi Winarko, and Ahmad Ashari. "Multi prime numbers principle to expand implementation of CRT method on RSA algorithm." In THE 2ND SCIENCE AND MATHEMATICS INTERNATIONAL CONFERENCE (SMIC 2020): Transforming Research and Education of Science and Mathematics in the Digital Age. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0041856.

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Rao, B. N. Prasad, and M. Rangamma. "An algorithm and a sieve to find prime numbers below 2n for given natural number n." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097530.

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Rosa, Rafael De la, Hilda Castillo, José C. Zavala, Alicia Martínez, and Hugo Estrada. "Application of prime numbers to solve complex instances of the bin packing problem." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4913025.

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K.R., Raghunandan, Ganesh Aithal, and Surendra Shetty. "Comparative Analysis of Encryption and Decryption Techniques Using Mersenne Prime Numbers and Phony Modulus to Avoid Factorization Attack of RSA." In 2019 International Conference on Advanced Mechatronic Systems (ICAMechS). IEEE, 2019. http://dx.doi.org/10.1109/icamechs.2019.8861599.

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Johansen, Stein E. "Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904611.

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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Department of Computer and Information Sciences, Northumbria University, 2019. http://dx.doi.org/10.21785/icad2019.003.

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The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0:5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematic

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Johansen, Stein E. "Negative approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from revolving geometric generation of natural numbers with recurrent outshooting leaving prime numbers." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904610.

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Thombre, Ritu, and Babita Jajodia. "Experimental Analysis of Attacks on RSA & Rabin Cryptosystems using Quantum Shor’s Algorithm." In International Conference on Women Researchers in Electronics and Computing. AIJR Publisher, 2021. http://dx.doi.org/10.21467/proceedings.114.74.

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In this world of massive communication networks, data security and confidentiality are of crucial importance for maintaining secured private communication and protecting information against eavesdropping attacks. Existing cryptosystems provide data security and confidentiality by the use of encryption and signature algorithms for secured communication. Classical computers use cryptographic algorithms that use the product of two large prime numbers for generating public and private keys. These classical algorithms are based on the fact that integer factorization is a non-deterministic polynomia

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