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

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

“…In this paper, instead of dealing with two prime numbers it is expanded to deal with n prime numbers. …”
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Modified Three-Dimensional Multicarrier Optical Prime Codes by Rajesh Yadav, Gurjit Kaur

“…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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A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms by B. L. Mayer, L. H. A. Monteiro

“…From this definition, the usual prime numbers correspond to the particular case d=2. …”
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On Some Properties of the Hofstadter–Mertens Function by Pavel Trojovský

“…In particular, as we shall see, this function encodes many interesting properties which relate prime numbers to “meta-sequences”.…”
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New proof and generalization of some results on translated sums over k-almost primes by Laib, Ilias

“…A sequence $\mathcal{A}$ of strictly positive integers is said to be primitive if none of its terms divides the others, Erdős conjectured that the sum $f(\mathcal{A},0)\le f(\mathbb{N}_{1},0),$ where $\mathbb{N}_{1}$ is the sequence of prime numbers and $f(\mathcal{A},h)=\sum _{a\,\in \,\mathcal{A}}$ $\frac{1}{a(\log a+h) }$. …”
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Cloud storage scheme based on closed-box encryption by Rui-zhong DU, Shao-xuan WANG, Jun-feng TIAN

“…Aiming at protecting the confidentiality of data for cloud storage users,a scheme that encrypt data in cloud service providers was presented.The scheme constructed a closed-box computing environment by virtual machine isolation technique,improved algorithm of RSA to change keys without having to produce large prime numbers,transfer data and keys through SSL and encrypted data in the closed computing environment before storing to the distributed file system.Closed-box computing environment can prevent attacks from cloud administrators and malicious applications in the operating system.It also can guard against data leakage effectively.The result of experiment shows that the confidentiality of data improved and the performance loss is decreased considering to other cloud storage scheme that encrypt data in cloud.…”
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RESEARCH OF PARAMETERS OF ENCODING OF THE ALGORITHM WITH VARIABLE FRAGMENTATION OF THE UNIT by K. O. Zakharova

“…Based on the results of the study of the operation of the algorithm with various encryption parameters (p and q), the following recommendations for the selection of parameters are formulated: p and q are mutually prime numbers, the partition of the sequence into p-subblocks is greater than the partition into q-subblocks (p &gt; q).…”
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On the emergence of the Quanta Prime sequence by Moustafa Ibrahim

“…The study uncovers profound connections between Quanta Prime numbers and essential sequences in number theory and cryptography. …”
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Symmetric Resonance Mechanism for Elimination of Parasitic Torque of a Permanent Magnet Generator under Stable Load by K. V. Dobrego, I. A. Koznacheev

“…Pi resonance is primarily realized in the case of a small difference in the values of Nr and Ns, which corresponds to the location near the main diagonal of the pi resonance table, as well as at the values of Nr, Ns corresponding to prime numbers. The number of configurations {Nr, Ns} providing pi resonance (compensation of parasitic torques) is the largest for the sinusoidal magnetic flux density and decreases if the magnetic flux density function is approximated by a high-degree Fourier series. …”
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Size, spines, and primes: the drivers of collar spine numbers among echinostome trematodes by Bronwen Presswell, Priscila M. Salloum, Jerusha Bennett, Katherine E. Buschang, Robert Poulin

“…First, we confirm that even numbers of spines are the norm among species in which they are arranged as 2 arcs with a central gap, while odd numbers (mainly prime numbers) predominate among species in which spines form a continuous collar. …”
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Pengamanan Pesan E-Complaint Fasilitas dan Kinerja Civitas Akademika Menggunakan Algoritma RSA by Dwi Yuny Sylfania, Fransiskus Panca Juniawan, Laurentinus Laurentinus, Hengki Hengki

“…The choice of RSA as a cryptographic algorithm is due to the difficulty of factoring prime numbers in key generation. This factoring will generate a public key for the message encryption process and a private key for the message decryption process. …”
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On Discrete Shifts of Some Beurling Zeta Functions by Antanas Laurinčikas, Darius Šiaučiūnas

“…We consider the Beurling zeta function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ζ</mi><mi mathvariant="double-struck">P</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>=</mo><mi>σ</mi><mo>+</mo><mi>i</mi><mi>t</mi></mrow></semantics></math></inline-formula>, of the system of generalized prime numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">P</mi></semantics></math></inline-formula> with generalized integers <i>m</i> satisfying the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>∑</mo><mrow><mi>m</mi><mo>⩽</mo><mi>x</mi></mrow></msub><mn>1</mn><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mi>x</mi><mi>δ</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><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><mn>0</mn><mo>⩽</mo><mi>δ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, and suppose that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ζ</mi><mi mathvariant="double-struck">P</mi></msub><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> has a bounded mean square for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>></mo><msub><mi>σ</mi><mi mathvariant="double-struck">P</mi></msub></mrow></semantics></math></inline-formula> with some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi mathvariant="double-struck">P</mi></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. …”
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