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Academic literature on the topic 'Mersenne'

Author: Grafiati

Published: 4 June 2021

Last updated: 22 February 2023

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Journal articles on the topic "Mersenne"

1

Granger, Robert. "Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test?" Mathematical Gazette 97, no. 539 (July 2013): 242–55. http://dx.doi.org/10.1017/s0025557200005830.

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The Lucas-Lehmer (LL) test is the most efficient known for testing the primality of Mersenne numbers, i.e. the integers Ml = 2l − 1, for l ≥ 1. The Mersenne numbers are so-called in honour of the French scholar Marin Mersenne (1588-1648), who in 1644 published a list of exponents l ≤ 257 which he conjectured produced all and only those Ml which are prime, for l in this range, namely l = 2,3,5,7, 13, 17, 19,31,67, 127 and 257 [1]. Mersenne's list turned out to be incorrect, omitting the prime-producing l = 61, 89 and 107 and including the composite-producing l = 67 and 257, although this was not finally confirmed until 1947, using both the LL test and contemporary mechanical calculators [2]. The LL test is based on the following theorem.

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Palmerino, Carla Rita. "Infinite Degrees of Speed Marin Mersenne and the Debate Over Galileo's Law of Free Fall." Early Science and Medicine 4, no. 4 (1999): 269–328. http://dx.doi.org/10.1163/157338299x00076.

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AbstractThis article analyzes the evolution of Mersenne's views concerning the validity of Galileo's theory of acceleration. After publishing, in 1634, a treatise designed to present empirical evidence in favor of Galileo's odd-number law, Mersenne developed over the years the feeling that only the elaboration of a physical proof could provide sufficient confirmation of its validity. In the present article, I try to show that at the center of Mersenne's worries stood Galileo's assumption that a falling body had to pass in its acceleration through infinite degrees of speed. His extensive discussions with, or his reading of, Descartes, Gassendi, Baliani, Fabri, Cazre, Deschamps, Le Tenneur, Huygens, and Torricelli led Mersenne to believe that the hypothesis of a passage through infinite degrees of speed was incompatible with any mechanistic explanation of free fall.

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Malcolm, Noel. "The Title of Hobbes's Refutation of Thomas White's De Mundo." Hobbes Studies 24, no. 2 (2011): 179–88. http://dx.doi.org/10.1163/187502511x597694.

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AbstractHobbes's manuscript refutation of Thomas White bears no title. Some modern scholars have proposed, on the basis of references to it by Mersenne, that the work was entitled 'De motu, loco et tempore', and the abbreviated version of this, 'De motu', has become current in modern scholarship. This research note analyses Mersenne's references, and concludes that this apparent title was a descriptive phrase introduced by Mersenne himself. The full description included the term 'philosophia' (thus: Hobbes's 'philosophy concerning motion, place and time'); this suggests a double focus, not only on the manuscript text, but also on Hobbes's 'body' of natural philosophy more generally.

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RAPHAEL, RENEE. "GALILEO'S DISCORSI AND MERSENNE'S NOUVELLES PENSEES: MERSENNE AS A READER OF GALILEAN 'EXPERIENCE'." Nuncius 23, no. 1 (2008): 7–36. http://dx.doi.org/10.1163/182539108x00012.

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Abstracttitle ABSTRACT /title This study examines Marin Mersenne's 1639 Nouvelles Pensees de Galilee, a translation and adaptation of Galileo Galilei's 1638 Discorsi. I use the translation as a window into how Mersenne, a reader trained in natural philosophy, read and understood Galileo's text and, in particular, Galileo's use of experience to support his claims. This analysis reveals that Mersenne drew on a variety of techniques and conceptions of experience in rendering Galileo's individual accounts of experience and experiment. The differences in the way the two authors relate discourse and experience is shown to be linked to their choices of genre and the varying motivations each brought to their texts.

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Berrizbeitia, Pedro, and Boris Iskra. "Gaussian Mersenne and Eisenstein Mersenne primes." Mathematics of Computation 79, no. 271 (March 3, 2010): 1779–91. http://dx.doi.org/10.1090/s0025-5718-10-02324-0.

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Daşdemir, Ahmet, and Göksal Bilgici. "Gaussian Mersenne numbers and generalized Mersenne quaternions." Notes on Number Theory and Discrete Mathematics 25, no. 3 (September 30, 2019): 87–96. http://dx.doi.org/10.7546/nntdm.2019.25.3.87-96.

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Özkan, Engin, and Mine Uysal. "Mersenne-Lucas hybrid numbers." Mathematica Montisnigri 52 (2021): 17–29. http://dx.doi.org/10.20948/mathmontis-2021-52-2.

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We introduce Mersenne-Lucas hybrid numbers. We give the Binet formula, the generating function, the sum, the character, the norm and the vector representation of these numbers. We find some relations among Mersenne-Lucas hybrid numbers, Jacopsthal hybrid numbers, Jacopsthal-Lucas hybrid numbers and Mersenne hybrid numbers. Then we present some important identities such as Cassini identities for Mersenne-Lucas hybrid numbers

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Descotes, Dominique. "Mersenne polémiste." Littératures classiques N° 59, no. 1 (2006): 93. http://dx.doi.org/10.3917/licla.059.0093.

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Matsumoto, Makoto, and Takuji Nishimura. "Mersenne twister." ACM Transactions on Modeling and Computer Simulation 8, no. 1 (January 1998): 3–30. http://dx.doi.org/10.1145/272991.272995.

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Haidar, Riad. "Marin Mersenne." Photoniques, no. 72 (July 2014): 17–19. http://dx.doi.org/10.1051/photon/20147217.

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Dissertations / Theses on the topic "Mersenne"

1

Talhah, Saad. "Advanced Encryption Techniques using New Mersenne Number Transforms." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.515408.

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Fabbri, Natacha. "De l’utilité de l'harmonie : Mersenne, Descartes e Galilei." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/86131.

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Duncan, David Allen. "The tyranny of opinions undermined : science, pseudo-science and scepticism in the musical thought of Marin Mersenne /." Ann Arbor : UMI, 2000. http://catalogue.bnf.fr/ark:/12148/cb37103406d.

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Basilico, Brenda. "Musique, mathématiques et philosophie dans l'oeuvre de Marin Mersenne." Thesis, Lille 3, 2017. http://www.theses.fr/2017LIL30038/document.

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Cette thèse doctorale prétend contribuer, premièrement, à soumettre à discussioncette interprétation dominante de la pensée philosophique et scientifique du PèreMinime Marin Mersenne (1588-1648), étant portée et structurée par la question duscepticisme, et deuxièmement, à mettre en avant la manière dont cette philosophieincarne l’esprit de la révolution scientifique du XVIIe siècle par sa capacité de se mettreen question dans sa recherche insatiable de la vérité; une recherche accompagnée d’unsouci de conservation de l’ordre politique et religieux. L’hypothèse principale de notretravail consiste à affirmer une profonde transformation dans la conception de la musique: transformation qui mène d’une science quadriviale et subalterne aux mathématiques,exigeant la soumission au jugement de la raison dans la pratique, à une science physiqueet mathématique, dont la recherche se fonde sur de nombreuses expériences,reconnaissant l’individualité de l’expérience esthétique, la liberté de l’imagination descompositeurs et le caractère ineffable du sublime musical. Il s’agit d’une transformationqui n’est pas exempte de difficultés, car elle ne conduit pas simplement à affirmerl’existence de deux périodes dans la pensée de Mersenne. En effet, il exprime ses doutessur la pertinence de l’approche spéculative lorsqu’il discute avec ses correspondants surla réforme musicale proposée à l’imitation des anciens et ne cesse de rappeler laperfection des rapports numériques des consonances lorsqu’il est prêt à les mettre enquestion en acceptant et en cherchant les fondements de la pratique de l’accordage desinstruments. Or, malgré cette complexité (voire ces contradictions) nous jugeons et nousprétendons montrer que cette transformation est indéniable et que l’épistémologie duMinime doit être analysée à la lumière des problématiques et de nouvelles expériencesscientifiques auxquelles il est confronté et non comme une manière de donner réponseaux arguments du scepticisme
This PhD dissertation provides a critical perspective of the dominantinterpretation of the scientific and philosophical works of Father Marin Mersenne(1588-1648) entirely structured by the sceptical question. The development of his ideasabout music embodies the spirit of the scientific revolution which emerges in theseventeenth-century. His investigation has the capacity to put his methods into questionwith an insatiable quest for the truth; a quest that involves political and religiousconcerns. The aim of this study is to show a profound transformation in the conceptionof music. This transformation that leads from a science of the quadrivium (subordinateto mathematics and claiming superiority of the judgement of reason) to a physical andmathematical science grounded on experience that recognizes the individuality of theesthetic experience, the liberty of the imagination of the composers and the ineffabilityof the sublime. It is quite difficult however to identify the existence of two differentstages in Mersenne’s thought. It is surprising how he expresses doubts about therelevance of the speculative approach to music whereas a musical reform is proposed inhis apologetic writings, having as a model the perfection of proportions of consonancesand rhythmic combinations well known by the ancients. And also, when he accepts thepractice of musical temperament, challenging the observation of the mathematicalperfection, he will continue to remind the proportions underlying the consonances.Despite this complexity (even these contradictions) we consider and pretend to showthat this transformation is undeniable and that the Mersenne epistemology must beanalysed according to the scientific questions and experiences which he faces in hisinvestigations and not as a response to a sceptical crisis

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Rutter, Nick. "Implementation and analysis of the generalised new Mersenne number transforms for encryption." Thesis, University of Newcastle upon Tyne, 2015. http://hdl.handle.net/10443/3236.

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Encryption is very much a vast subject covering myriad techniques to conceal and safeguard data and communications. Of the techniques that are available, methodologies that incorporate the number theoretic transforms (NTTs) have gained recognition, specifically the new Mersenne number transform (NMNT). Recently, two new transforms have been introduced that extend the NMNT to a new generalised suite of transforms referred to as the generalised NMNT (GNMNT). These two new transforms are termed the odd NMNT (ONMNT) and the odd-squared NMNT (O2NMNT). Being based on the Mersenne numbers, the GNMNTs are extremely versatile with respect to vector lengths. The GNMNTs are also capable of being implemented using fast algorithms, employing multiple and combinational radices over one or more dimensions. Algorithms for both the decimation-in-time (DIT) and -frequency (DIF) methodologies using radix-2, radix-4 and split-radix are presented, including their respective complexity and performance analyses. Whilst the original NMNT has seen a significant amount of research applied to it with respect to encryption, the ONMNT and O2NMNT can utilise similar techniques that are proven to show stronger characteristics when measured using established methodologies defining diffusion. Analyses in diffusion using a small but reasonably sized vector-space with the GNMNTs will be exhaustively assessed and a comparison with the Rijndael cipher, the current advanced encryption standard (AES) algorithm, will be presented that will confirm strong diffusion characteristics. Implementation techniques using general-purpose computing on graphics processing units (GPGPU) have been applied, which are further assessed and discussed. Focus is drawn upon the future of cryptography and in particular cryptology, as a consequence of the emergence and rapid progress of GPGPU and consumer based parallel processing.

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Psychoyou, Theodora. "L'évolution de la pensée théorique en France, de Marin Mersenne à Jean-Philippe Rameau." Tours, 2003. http://www.theses.fr/2003TOUR2036.

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La matière de cette thèse vient de 261 écrits sur la musique décrits (2d vol. ) dans un catalogue systématique (notices et index). Le 1er vol. Est nécessaire à l'étude des aspects fondamentaux du corpus : les modèles de la théorie musicale. Le discours sur la musique est étudié du point de vue de la distance qu'il prend de l'héritage du passé (antique, médiéval, humaniste) : de l'appropriation de cet héritage et de ses avatars. La multitude des modèles potentiels, de leurs interprétations, puis des finalités et des approches des auteurs, génére plusieurs confrontations : Anciens/modernes, théoriciens/praticiens, Français/italiens. Ces visions bipolaires de la musique témoignent de l'impossibilité de la circonscrire par un discours propre. Sont ensuite examinés les liens entre la musique et la science, notamment les aspects de sa codification théorique, telles la compréhension spectrale du son, l'étude des tempéraments musicaux, les recherches d'étalons du temps et de la hauteur.

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BALDIN, GREGORIO. "Una visione del mondo meccanicista: Galileo e Mersenne nella filosofia naturale di Thomas Hobbes." Doctoral thesis, Università del Piemonte Orientale, 2015. http://hdl.handle.net/11579/81616.

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Taveau, Laurence. "Le manuscrit 2884 du Père Mersenne à la bibliothèque de l’Arsenal. Étude et édition critique." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUL046.

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Le manuscrit 2884 est un autographe du père Mersenne, unique exemplaire conservé à la bibliothèque de l’Arsenal. Cet écrit constitué en livre et chapitres est une théorie spéculative du son et des consonances inachevée. Comme le manuscrit n’a jamais été édité nous en proposons la transcription selon deux pratiques différentes, une selon le modèle de l’École nationale des Chartes et l’autre diplomatique selon le laboratoire de l’ITEM spécialisé dans les brouillons d’écriture. La transcription est complétée par des notes critiques et historiques, une table des théorèmes reconstituée, d’un index des noms propres. Le fac-simile du manuscrit est proposé dans un volume à part. Dans la première partie une étude codicologique permet de situer le manuscrit dans son aspect matériel. Une étude génétique détermine ses liens avec les imprimés du père Mersenne et retrace son parcours général de rédaction. La dernière partie de la thèse tente de cerner les motifs de son abandon par une analyse comparative avec quelques livres de l’Harmonie Universelle. Notre hypothèse de départ repose sur un changement de philosophie naturelle, passage de la philosophie aristotélicienne à la philosophie d’inspiration galiléenne. En effet nous montrons que tout le discours tenu dans le manuscrit 2884 est ontologiquement fondé dans la conception aristotélicienne alors que les mêmes sujets abordés dans l’Harmonie Universelle manifestent une rupture avec ce fondement ontologique ainsi qu’une profonde évolution de ses idées
Manuscript 2884 is an autograph by Marin Mersenne, a unique document preserved in the Arsenal Library. This writing formed of books and chapters is an unfinished speculative theory of sound and consonance. As the manuscript has never been edited we propose a transcription following two different usages, the first according to the model of the École nationale des Chartes and the second a diplomatic transcription according to the laboratory of the ITEM (Institut des Textes et Manuscrits modernes) specializing in drafts of texts. The transcriptions are supplemented by critical and historical notes, a reconstructed table of theorems and an index of proper names. The facsimile of the manuscript is proposed in a separate volume. In the first part, a codicological study makes it possible to describe the manuscript in its material aspect. A genetic study determines its links with the printed works of Marin Mersenne and traces its general course of writing. The last part of the thesis attempts to define the reasons for its abandonment by a comparative analysis with some books of Harmonie Universelle. Our initial hypothesis supposes a change in natural philosophy, a change from Aristotelian philosophy to a philosophy of Galilean inspiration. We show that the discourse held in manuscript 2884 as a whole is ontologically based in the Aristotelian conception whereas the same subjects approached in Harmonie Universelle show a break with this ontological foundation as well as a profound evolution of Mersenne’s ideas

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Hettche, Matthew. "Regarding Descartes' meditations as meditational." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-06102009-063446/.

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Buccolini, Claudio. ""Rem totam more geometrico concludas" : La recherche d'une preuve mathématique de l'existence de Dieu chez Marin Mersenne." Paris, EPHE, 2003. http://www.theses.fr/2003EPHE5065.

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Books on the topic "Mersenne"

1

Beaulieu, Armand. Mersenne: Le grand minime. Bruxelles: Fondation Nicolas-Claude Fabri de Peiresc, 1995.

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Maury, Jean-Pierre. A l'origine de la recherche scientifique, Mersenne. Paris: Vuibert, 2003.

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Sylvie, Taussig, ed. A l'origine de la recherche scientifique: Mersenne. Paris: Vuibert, 2003.

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Mersenne, Marin. Correspondance du P. Marin Mersenne, religieux minime. Paris: Éditions du C.N.R.S., 1986.

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Mersenne, Marin. Correspondance du P. Marin Mersenne, religieux minime. Paris: Éditions du C.N.R.S., 1988.

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Mersenne and the learning of the schools. Ithaca: Cornell University Press, 1988.

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De l'utilité de l'harmonie: Filosofia, scienza e musica in Mersenne, Descartes e Galileo. Pisa: Edizioni della Normale, 2008.

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Fabbri, Natacha. Cosmologia e armonia in Kepler e Mersenne: Contrappunto a due voci sul tema dell'harmonice mundi. Firenze: L.S. Olschki, 2003.

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Köhler, Wolfgang. Die Blasinstrumente aus der "Harmonie universelle" des Marin Mersenne: Übersetzung und Kommentar des "Livre cinquiesme des instrumens à vent" aus dem "Traité des instruments". Celle: Moeck, 1987.

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Negwer, Ingo. Laute und Theorbe in Marin Mersennes Harmonie universelle: Zur Aufführungspraxis frühbarocker Musik in Frankreich. Frankfurt am Main: Deutsche Lautengesellschaft, 2000.

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Book chapters on the topic "Mersenne"

1

Barnes, John. "Mersenne." In Nice Numbers, 303–23. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46831-0_19.

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Fabbri, Natacha. "Mersenne, Marin." In Encyclopedia of Early Modern Philosophy and the Sciences, 1–12. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-20791-9_150-1.

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Caldwell, Chris K. "Mersenne, Marin." In Biographical Encyclopedia of Astronomers, 1462–63. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4419-9917-7_941.

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Hall, Graham, Ian Elliott, Mihkel Joeveer, Fabrizio Bònoli, Y. Tzvi Langermann, Josep Casulleras, Ke Ve Sarma, et al. "Mersenne, Marin." In The Biographical Encyclopedia of Astronomers, 772–73. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-30400-7_941.

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Solinas, Jerome A. "Mersenne Prime." In Encyclopedia of Cryptography and Security, 774–75. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_37.

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Fabbri, Natacha. "Mersenne, Marin." In Encyclopedia of Early Modern Philosophy and the Sciences, 1312–23. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-319-31069-5_150.

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Solinas, Jerome A. "Generalized Mersenne Prime." In Encyclopedia of Cryptography and Security, 509–10. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_32.

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Solinas, Jerome A. "Pseudo-Mersenne Prime." In Encyclopedia of Cryptography and Security, 992. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_42.

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Baldin, Gregorio. "Hobbes and Mersenne." In International Archives of the History of Ideas Archives internationales d'histoire des idées, 1–51. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41414-6_1.

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Kleinjung, Thorsten, Joppe W. Bos, and Arjen K. Lenstra. "Mersenne Factorization Factory." In Lecture Notes in Computer Science, 358–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-45611-8_19.

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Conference papers on the topic "Mersenne"

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Thall, Andrew. "Fast Mersenne prime testing on the GPU." In the Fourth Workshop. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1964179.1964188.

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Mellon, Russell R., Daniel L. Scheld, and Robert E. Stencel. "Afocal Mersenne telescope for teaching and research." In Astronomical Telescopes and Instrumentation, edited by Jacobus M. Oschmann and Larry M. Stepp. SPIE, 2003. http://dx.doi.org/10.1117/12.458674.

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Kehil, Djamel, and Youcef Ferdi. "Signal encryption using new Mersenne number transform." In 2010 7th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP 2010). IEEE, 2010. http://dx.doi.org/10.1109/csndsp16145.2010.5580327.

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Tiepelt, Marcel, and Jan-Pieter D'Anvers. "Exploiting Decryption Failures in Mersenne Number Cryptosystems." In ASIA CCS '20: The 15th ACM Asia Conference on Computer and Communications Security. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3384940.3388957.

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Bouche, Thierry, Evelyne Miot, and Célia Vaudaine. "The Centre Mersenne, one year of operation." In ELPUB 2019 23d International Conference on Electronic Publishing. OpenEdition Press, 2019. http://dx.doi.org/10.4000/proceedings.elpub.2019.14.

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Bos, Joppe W., Thorsten Kleinjung, Arjen K. Lenstra, and Peter L. Montgomery. "Efficient SIMD Arithmetic Modulo a Mersenne Number." In 2011 IEEE 20th Symposium on Computer Arithmetic (ARITH). IEEE, 2011. http://dx.doi.org/10.1109/arith.2011.37.

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Balonin, Nickolay A., and Mikhail B. Sergeev. "On existence of Mersenne and Hadamard matrices." In 2014 XIV International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY). IEEE, 2014. http://dx.doi.org/10.1109/red.2014.7016697.

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Daghigh, Hassan, Amir Mehdi Yazdani kashani, and Ruholla Khodakaramian Gilan. "Primality test for mersenne numbers using elliptic curves." In 2014 11th International ISC Conference on Information Security and Cryptology (ISCISC). IEEE, 2014. http://dx.doi.org/10.1109/iscisc.2014.6994029.

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Chandrasekaran, Shrutisagar, and Abbes Amira. "High Performance FPGA Implementation of the Mersenne Twister." In 4th IEEE International Symposium on Electronic Design, Test and Applications (delta 2008). IEEE, 2008. http://dx.doi.org/10.1109/delta.2008.113.

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Conway, R. "Reduced complexity filtering using Fermat and Mersenne transforms." In IEE Irish Signals and Systems Conference 2005. IEE, 2005. http://dx.doi.org/10.1049/cp:20050302.

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Reports on the topic "Mersenne"

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Burchell, Timothy. MERSEN GRADE 2114: A COMPARISON OF TENSILE STRENGTH DATA. Office of Scientific and Technical Information (OSTI), February 2020. http://dx.doi.org/10.2172/1905428.

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