Results 1 to 10 of about 12,813,623 (299)
Weighted Prime Number Theorem on Arithmetic Progressions with Refinements
MathematicsWe present an extension of the Dirichlet-type prime number theorem to weighted counting functions, the importance of which has recently been recognized for formulating Chebyshev’s bias.
Koji Shimada, Shin-ya Koyama
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Pseudo-prime number simulation and its application for security purpose
MATEC Web of Conferences, 2018 Many public cryptography schemes rely on the use of prime numbers like for encryption and decryption. A prime number is one number that is widely used and large and consists of hundreds of digits, so it takes time to test whether the numbers are prime or
Rahim Robbi +10 more
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Holographic realization of the prime number quantum potential. [PDF]
PNAS Nexus, 2023 Cassettari D, Mussardo G, Trombettoni A.
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The Fractal Nature of an Approximate Prime Counting Function
Fractal and Fractional, 2017 Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function.
Dimitris Vartziotis, Joachim Wipper
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Arab Journal of Basic and Applied SciencesThis paper introduces a new key geometric way to understand Mersenne prime numbers. It discovers a shape called the Mersenne Star, which appears naturally from a special sequence named the Quanta Prime Sequence (QPS).
Moustafa Ibrahim
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MathematicsDetermining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable.
Timothy Ganesan
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The condition number associated with ideal lattices from odd prime degree cyclic number fields
Journal of Mathematical CryptologyThe condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the ...
de Araujo Robson Ricardo
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Blade prime-number / uniform angular distribution criterion for vibration reduction
Engineering TransactionsCurrently, the vibration noise of casting cleaning equipment exceeds 95 dB, which not only impacts the equipment's service life but also jeopardizes workers' health.
Yong Li +5 more
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International Journal for Innovation Education and Research, 2017 A prime number is a natural number that has Just two divisors: one and itself. From antiquity until our time, scientists are researching mathematical reasoning to understand the prime numbers; eminent scholars had worked on this field before it is abandoned. Mathematicians considered the prime numbers like « building blocs in building natural numbers »
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Prime number factorization with light beams carrying orbital angular momentum
APL PhotonicsWe point out a link between orbital angular momentum (OAM) carrying light beams and number theory. The established link makes it possible to formulate and implement a simple and ultrafast protocol for prime number factorization by employing OAM endowed ...
Xiaofei Li +6 more
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