A Visual Display of Some Properties of the Distribution of Primes

Stein, M. L.; Ulam, Stanislaw M.; Wells, Mark B.

doi:10.2307/2312588

Cited by 42 publications

(35 citation statements)

References 2 publications

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“…Indeed, the first recurrence happens with the isotopes of Ti with neutron excess numbers of A − 2Z = 2, 3, 4, 5 -a uniform increase of four units over the neutron numbers of the starting set, and it coincides with the completion of the second set of 24 on the 24 × 11 matrix [5]. Two further exact coincidences occur with four isotopes of Sn (A − 2Z = 14,15,16,17) and of Os (A − 2Z = 34, 35, 36, 37), closing periods 6 and 10, respectively.…”

Section: Nuclidic Periodicitymentioning

confidence: 96%

“…A much celebrated computer-generated graphic that appears to reveal a mysterious regularity in the distribution of prime numbers was published some time ago [17], made it to the cover of Scientific American [19] and features on many websites [18]. It is known as a prime-number spiral and the positions of primes show up visibly along lines, parallel to the main diagonals of the dense spiral.…”

Section: Distribution Of Prime Numbersmentioning

confidence: 99%

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Number Theory and the Periodicity of Matter

Boeyens

Levendis

2008

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Section: Nuclidic Periodicitymentioning

confidence: 96%

Section: Distribution Of Prime Numbersmentioning

confidence: 99%

Number Theory and the Periodicity of Matter

Boeyens

Levendis

2008

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“…Ulam used a square spiral to visualize the prime numbers and discovered that they form straight lines in some areas [37]. For example, 4x…”

Section: Square Spiral Encodingmentioning

confidence: 99%

Assignment as a location-based service in outsourced databases

Büyükkayhan¹,

Gündem²

2017

Turk J Elec Eng & Comp Sci

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Abstract:Location-based services provide opportunities to organizations for tracking and utilizing their resources. Moreover, some corporations prefer to outsource their database management services. In the literature, privacy preservation techniques in outsourced spatial databases for several query types, such as nearest neighbor, K-nearest neighbor, and proximity search, have been examined. In this paper, we present an efficient application of the capacity and coverageconstrained assignment query on outsourced spatial databases. In the proposed technique, we introduce a novel spatial transformation strategy (square spiral encoding) to achieve privacy efficiently for approximate assignment query results.To process the assignment query, we use the parallel auction algorithm. We implemented and tested the assignment query with the proposed technique for correctness and efficiency.

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“…The Prime Number Theorem, which establishes the global smoothness of the counting function π(n) by providing the number of primes less or equal to the integer n, was the first indication of such regularity [16]. Some other prime patterns have been found and advanced so far, from the visual Ulam Spiral [17] to the arithmetic progression of primes [18]. Some other patterns remain conjectures, such as the global gap distribution between primes or the twin primes distribution [16], enhancing the enigmatic interplay between apparent randomness and hidden regularity.…”

Section: A Statistical Pattern In the Prime Number Sequencementioning

confidence: 99%

Complex Systems, Numbers and Number Theory

Lacasa¹,

Luque²,

Miramontes³

2010

Reviews of Nonlinear Dynamics and Complexity

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All is number. PythagorasMuch ink has dried in the historical discussion of what is mathematics? Does it follows the scientific method? Is it just a collection of recipes, formulas and algorithms? Is it a science or a tool for others to use? Is it both? Carl Friedrich Gauss, one of the greatest mathematicians of all times called, it The Queen of Sciences but it was Eric Temple Bell who named it as Queen and Servant of Science in the title of one of his most celebrated books [1]. To some, this is an adequate way of expressing this dichotomy on the nature of mathematics and of its practical role ahead of other sciences [2]. There is, however, an aspect often neglected in all this discussion which is related to mathematics seen as natural phenomena and so susceptible of study by other sciences, such as physics. Do numbers along with their arithmetic operations behave as physical systems? More specifically, can the modern theory of nonlinear physics address number arithmetics as complex physical phenomena? From the remarkable coincidence in 1972 between H. Montgomery's work on the statistics of the spacings between zeta zeros and F. Dyson's analogous work on eigenvalues of random matrices, we have seen, somewhat unexpectedly, how number theory and physics have tended bridges between each other. These connections range from the reinterpretation of the Riemann zeta function as a partition function [3] or the focus of the Riemann Hypothesis via quantum chaos [4][5][6], to multifractality in the distribution of primes [7] or computational phase transitions in the number partitioning problem [8], to cite but a few (see [9] for an extensive bibliography).

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A Visual Display of Some Properties of the Distribution of Primes

Cited by 42 publications

References 2 publications

Number Theory and the Periodicity of Matter

Number Theory and the Periodicity of Matter

Assignment as a location-based service in outsourced databases

Complex Systems, Numbers and Number Theory

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