Construction and count of resilient rotation symmetric Boolean functions with prime number variables by Jiao DU, Qiao-yan WEN, Jie ZHANG, Shan-qi PANG

“…A necessary and sufficient condi-tion on the construction of resilient RSBF with prime number variables was derived. So construction and count formula of all the resilient RSBF with prime number variables were determined by this way. …”
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Prime-number-assisted block-based neighbor discovery protocol in wireless sensor networks by Woosik Lee, Jong-Hoon Youn, Teukseob Song

“…For example, for two sensors whose duty cycles are different, if the lengths of their discovery schedules are relatively prime, the prime-number-assisted block-based neighbor discovery protocol simply uses the balanced incomplete block design–based neighbor discovery protocol without adding any additional active slots; otherwise, it changes the original balanced incomplete block design–based schedule using a prime number. …”
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A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories by M. Abdel-Mageed, Ahmed Salim, Walid Osamy, Ahmed M. Khedr

“…The distributions are made up of sequences of prime numbers from one hundred to three hundred and fifty million prime numbers. …”
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On the K-th extension of the Sieve of eratosthenes by Antonio R. Quesada

Subjects: “…prime numbers…”
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Unique gating strategy identifier based on the Prime Population System and Gödel Numbers by Antonio Cosma

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Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur befor 1012 by Carter Bays, Richard H. Hudson

Subjects: “…prime numbers…”
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Differences between powers of a primitive root by Marian Vâjâitu, Alexandru Zaharescu

“…We study the set of differences {gx−gy(modp):1≤x,   y≤N} where p is a large prime number, g is a primitive root (modp), and p2/3<N<p.…”
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Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups by Khuanchanok Chaichana, Pradthana Jaipong

“…In this study, we work on the Fuchsian group Hm where m is a prime number acting on mℚ^ transitively. We give necessary and sufficient conditions for two vertices to be adjacent in suborbital graphs induced by these groups. …”
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A New Nonlinear Equation with Lump-Soliton, Lump-Periodic, and Lump-Periodic-Soliton Solutions by Bo Ren, Ji Lin, Zhi-Mei Lou

“…An extended (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff-like equation is proposed by using the generalized bilinear operators based on a prime number p=3. By combining multiexponential functions with a quadratic function, the interaction between lumps and multikink soliton is generated. …”
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Further Results on a Curious Arithmetic Function by Long Chen, Kaimin Cheng, Tingting Wang

“…Let p be an odd prime number and n be a positive integer. Let vpn, N∗, and Q+ denote the p-adic valuation of the integer n, the set of positive integers, and the set of positive rational numbers, respectively. …”
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Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two by Xia Zhou

“…Suppose that p and q are two distinct odd prime numbers with n=pq. In this paper, the uniform representation of general two-prime generalized cyclotomy with order two over ℤn was demonstrated. …”
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Some special cases on Stolarsky’s means by Cesare Palmisani

“…We link SM having the integer power of a prime number as a parameter to classical means (i.e., harmonic mean, geometric mean, arithmetic mean, power mean). …”
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Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH by Daniel Cervantes‐Vázquez, Eduardo Ochoa‐Jiménez, Francisco Rodríguez‐Henríquez

“…SIDH operates on supersingular elliptic curves defined over Fp2, where p is a large prime number of the form p=4eA3eB−1 and eA and eB are positive integers such that 4eA≈3eB. …”
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Finite Local Rings of Length 4 by Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori

“…This paper presents a comprehensive characterization of finite local rings of length 4 and with residue field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>,</mo></mrow></semantics></math></inline-formula> where <i>p</i> is a prime number. Such rings have an order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>p</mi><mrow><mn>4</mn><mi>m</mi></mrow></msup></semantics></math></inline-formula> elements. …”
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Prospects for the Use of Quasi-Mersen Numbers in the Design of Parallel-Serial Processors by Aruzhan Kadyrzhan, Kaisarali Kadyrzhan, Akhat Bakirov, Ibragim Suleimenov

“…Such a set of prime numbers satisfies the criterion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msub><mi>p</mi><mn>1</mn></msub><msub><mi>p</mi><mn>2</mn></msub><msub><mi>p</mi><mn>3</mn></msub><msub><mi>p</mi><mn>4</mn></msub><mo>+</mo><mn>1</mn><mo>=</mo><mi>P</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula> is also a prime number. …”
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Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization by Leonid G. Fel

“…We consider a wide class of summatory functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mfenced separators="" open="{" close="}"><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced><mo>=</mo><msub><mo>∑</mo><mrow><mi>k</mi><mo>≤</mo><mi>N</mi></mrow></msub><mi>f</mi><mfenced separators="" open="(" close=")"><msup><mi>p</mi><mi>m</mi></msup><mi>k</mi></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula> associated with the multiplicative arithmetic functions <i>f</i> of a scaled variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>∈</mo><msub><mi mathvariant="double-struck">Z</mi><mo>+</mo></msub></mrow></semantics></math></inline-formula>, where <i>p</i> is a prime number. Assuming an asymptotic behavior of the summatory function, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>{</mo><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mover><mo>=</mo><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></mover><msub><mi>G</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mfenced separators="" open="[" close="]"><mn>1</mn><mo>+</mo><mi mathvariant="script">O</mi><mfenced separators="" open="(" close=")"><msub><mi>G</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mfenced></mfenced></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>N</mi><msub><mi>a</mi><mn>1</mn></msub></msup><msup><mfenced separators="" open="(" close=")"><mi>log</mi><mi>N</mi></mfenced><msub><mi>b</mi><mn>1</mn></msub></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>N</mi><mrow><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub></mrow></msup><msup><mfenced separators="" open="(" close=")"><mi>log</mi><mi>N</mi></mfenced><mrow><mo>−</mo><msub><mi>b</mi><mn>2</mn></msub></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><msub><mi>a</mi><mn>2</mn></msub><mo>≥</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mo>∞</mo><mo><</mo><msub><mi>b</mi><mn>1</mn></msub><mo>,</mo><msub><mi>b</mi><mn>2</mn></msub><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>, we calculate the renormalization function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mfenced separators="" open="(" close=")"><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced></mrow></semantics></math></inline-formula>, defined as a ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mfenced separators="" open="{" close="}"><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced><mo>/</mo><mi>F</mi><mrow><mo>{</mo><mi>f</mi><mo>;</mo><mi>N</mi><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula>, and find its asymptotics <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mo>∞</mo></msub><mfenced separators="" open="(" close=")"><mi>f</mi><mo>;</mo><msup><mi>p</mi><mi>m</mi></msup></mfenced></mrow></semantics></math></inline-formula> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. …”
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A Simple Algorithm for Prime Factorization and Primality Testing by Kabenge Hamiss

“…We propose a new simple and faster algorithm to factor numbers based on the nature of the prime numbers contained in such composite numbers. It is well known that every composite number has a unique representation as a product of prime numbers. …”
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Factorization of big integer and the security of RSA by Yan-bing REN

“…Three kinds of methods for integer factorization were proposed and the security of RSA was demarcated.RSA is a well-known cryptographic algorithm,using the analysis result of those methods.Through the work,readers could easily realize that if merely enlarged two prime numbers but lost attention of the relevance of them,the security of this algorithm might been missed.In the end,two recommended tactics to choose prime numbers as key of this algorithm were given.…”
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Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral by Tim Johnson

“…Ulam’s spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. …”
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A Novel Approach for Safeguarding Kurdish Text Files via Modified AES-OTP and Enhanced RSA Cryptosystem on Unreliable Networks by Newroz Nooralddin Abdulrazaq

“…The modified RSA cipher system is based on randomly selecting two large co-prime numbers under the restriction, each having at most two factors, instead of two large prime numbers.…”
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