Results 11 to 20 of about 11,676,412 (344)
Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions [PDF]
Duke mathematical journal, 2020 We establish two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg, a theorem of Erdős-Delange, the mean value theorem of ...
V. Bergelson, F. Richter
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A new elementary proof of the Prime Number Theorem [PDF]
Bulletin of the London Mathematical Society, 2020 Let Ω(n) denote the number of prime factors of n . We show that for any bounded f:N→C one has 1N∑n=1Nf(Ω(n)+1)=1N∑n=1Nf(Ω(n))+oN→∞(1).This yields a new elementary proof of the Prime Number Theorem.
F. Richter
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ALTERNATIVE PROOF OF THE INFINITUDE PRIMES AND PRIME PROPERTIES
Barekeng, 2023 Prime numbers is one of kind number that have many uses, one of which is cryptography. The uniqueness of prime numbers in their divisors and distributions causes prime numbers to be widely used in digital security systems. In number theory, one of famous
Dinni Rahma Oktaviani +2 more
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Properties of Higher-Order Prime Number Sequences [PDF]
Missouri Journal of Mathematical Sciences, 2020 In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic selection and ...
Michael P. May
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Blockchain Security Mechanism Design Based on Chinese Cryptosystem SM2 Algorithm
Mathematics, 2023 The cryptographic system is the foundation of blockchain security mechanisms. This paper constructs a blockchain security mechanism based on the Chinese national cryptographic SM2 algorithm, involving the generation of public–private key pairs and the ...
Lu Meng, Zeyao Liu
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The error term in the prime number theorem [PDF]
Mathematics of Computation, 2018 We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing
David J. Platt, Timothy S. Trudgian
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On the number of edges of a graph and its complement [PDF]
Arab Journal of Mathematical Sciences, 2021 Let G=(V,E) be a graph. The complement of G is the graph G¯:=(V,[V]2 \ E) where [V]2 is the set of pairs {x,y} of distinct elements of V. If K is a subset of V, the restriction of G to K is the graph G↾K:=(K,[K]2∩E).
Jamel Dammak +2 more
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On the Universal Encoding Optimality of Primes
Mathematics, 2021 The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows
Ioannis N. M. Papadakis
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Relation between Prime and Composite Number
Bibechana, 2018 This article was not peer-reviewed. No abstract available.
Raju Ram Thapa
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Prime Slaughter: Playful Prime Numbers [PDF]
, 2012 Starting from the difficulty of creating playful representation of domain-specific abstract concepts, this study discusses the design of Prime Slaughter, a computer game aimed at facilitating individual sense-making of abstract mathematical concepts. Specifically the game proposes a transposition of primality and factorization into playful interactions,
Valente, Andrea, Marchetti, Emanuela
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