Results 11 to 20 of about 93,875 (269)
Entropy, Periodicity and the Probability of Primality [PDF]
EntropyThe distribution of prime numbers has long been viewed as a balance between order and randomness. In this work, we investigate the relationship between entropy, periodicity, and primality through the computational framework of the binary derivative.
Grenville J. Croll
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The Sampling Distribution of Primes [PDF]
Proceedings of the National Academy of Sciences, 1963 This paper was communicated to the journal by H. S. Vandiver, number theorist and fellow of the US National Academy of Sciences.
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Machine learning of the prime distribution [PDF]
PLOS ONEIn the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy–Ramanujan Theorem. We also provide a theoretical argument explaining the experimental observations of Y.–H. He about the learnability of primes, and posit that the Erdős–Kac law would very unlikely be discovered
Alexander Kolpakov, A. Alistair Rocke
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, 2000 In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of
Saidak, F.
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Distribution of Square-Prime Numbers
Missouri Journal of Mathematical Sciences, 2022 For $a \neq 1$ and $p$ prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) Numbers. For example, 75 = 3 $\cdot$ 25; 108 = 3 $\cdot$ 36; 45 = 5 $\cdot$ 9. These numbers are listed in the OEIS as A228056. We study the properties of these numbers, their distribution/density and also develop a few claims on their distribution/density.
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The Density of Primes Less or Equal to a Positive Integer up to 20,000: Fractal Approximation
Recoletos Multidisciplinary Research Journal, 2013 The highly irregular and rough fluctuations of the number of primes less or equal to a positive integer x for smaller values of x ( x≤20,000) renders the approximations through the Prime Number Theorem quite unreliable. A fractal probability distribution
Rodel B. Azura +3 more
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A note on Chebyshev's theorem [PDF]
Notes on Number Theory and Discrete MathematicsWe revisit a classical theorem of Chebyshev about distribution of primes on intervals (n, 2n), n∈ℕ, and prove a generalization of it. Extending Erdős' arithmetical-combinatorial argument, we show that for all k∈ℕ, there is nₖ∈ℕ such that the intervals ...
A. Bërdëllima
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Modeling the Dirichlet distribution using multiplicative functions
Nonlinear Analysis, 2020 For q,m,n,d ∈ N and some multiplicative function f > 0, we denote by T3(n) the sum of f(d) over the ordered triples (q,m,d) with qmd = n. We prove that Cesaro mean of distribution functions defined by means of T3 uniformly converges to the one-parameter ...
Gintautas Bareikis, Algirdas Mačiulis
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Amodal completion of partly occluded figures: Effect of contour orientation [PDF]
Psihologija, 2003 In present study the temporal dimension of amodal completion in visual occlusion was investigated. We supposed that the visual system prefers to complete normally (vertically-horizontally) oriented contours than the oblique ones. Using the prime-matching
Marković Slobodan S. +1 more
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Elliptic curves with a given number of points over finite fields [PDF]
, 2013 Given an elliptic curve $E$ and a positive integer $N$, we consider the problem of counting the number of primes $p$ for which the reduction of $E$ modulo $p$ possesses exactly $N$ points over $\mathbb F_p$. On average (over a family of elliptic curves),
Chantal David +6 more
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