Showing 1 - 20 results of 27 for search '"prime number"', query time: 0.06s Refine Results
  1. 1

    Prime-number-assisted block-based neighbor discovery protocol in wireless sensor networks by Woosik Lee, Jong-Hoon Youn, Teukseob Song

    Published 2019-01-01
    “…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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  2. 2

    On the K-th extension of the Sieve of eratosthenes by Antonio R. Quesada

    Published 1995-01-01
    Subjects: “…prime numbers…”
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    Differences between powers of a primitive root by Marian Vâjâitu, Alexandru Zaharescu

    Published 2002-01-01
    “…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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  6. 6

    Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups by Khuanchanok Chaichana, Pradthana Jaipong

    Published 2019-01-01
    “…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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  7. 7

    A New Nonlinear Equation with Lump-Soliton, Lump-Periodic, and Lump-Periodic-Soliton Solutions by Bo Ren, Ji Lin, Zhi-Mei Lou

    Published 2019-01-01
    “…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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  8. 8

    Further Results on a Curious Arithmetic Function by Long Chen, Kaimin Cheng, Tingting Wang

    Published 2020-01-01
    “…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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  9. 9

    Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two by Xia Zhou

    Published 2020-01-01
    “…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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  10. 10

    Some special cases on Stolarsky’s means by Cesare Palmisani

    Published 2024-12-01
    “…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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  11. 11

    Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH by Daniel Cervantes‐Vázquez, Eduardo Ochoa‐Jiménez, Francisco Rodríguez‐Henríquez

    Published 2021-09-01
    “…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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  12. 12

    Finite Local Rings of Length 4 by Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori

    Published 2024-12-01
    “…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

    Published 2025-01-01
    “…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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  14. 14

    Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization by Leonid G. Fel

    Published 2025-01-01
    “…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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  15. 15

    A Simple Algorithm for Prime Factorization and Primality Testing by Kabenge Hamiss

    Published 2022-01-01
    “…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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  16. 16

    Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral by Tim Johnson

    Published 2023-01-01
    “…Ulam’s spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. …”
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  17. 17

    A Novel Approach for Safeguarding Kurdish Text Files via Modified AES-OTP and Enhanced RSA Cryptosystem on Unreliable Networks by Newroz Nooralddin Abdulrazaq

    Published 2024-06-01
    “…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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  18. 18

    On a Diophantine Inequality with s Primes by Xiaofei Yan, Lu Zhang

    Published 2021-01-01
    “…In this study, for prime numbers p1,…,ps and a sufficiently large real number N, we prove the Diophantine inequality p1c+⋯+psc−N<N−9/10cδ−c, where δ=294−210s/123−97s and s≥5. …”
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  19. 19

    An improved Fully Homomorphic Encryption model based on N-Primes by Mohammed Anwar Mohammed, Fadhil Salman Abed

    Published 2019-10-01
    “…In this paper, instead of dealing with two prime numbers it is expanded to deal with n prime numbers. …”
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  20. 20

    Modified Three-Dimensional Multicarrier Optical Prime Codes by Rajesh Yadav, Gurjit Kaur

    Published 2016-01-01
    “…The proposed model has been extensively simulated on MATLAB for prime numbers (P) to analyze the performance of code in terms of autocorrelation and cross-correlation. …”
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