منابع مشابه
Quotients of Gaussian Primes
It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: “Is the set of all quotients of Gaussian primes dense in the complex plane?” Quotient sets {s/t : s, t ∈ S} corresponding to subsets S of the natural numbers have been intensely studied in the...
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The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
متن کاملA Stroll Through the Gaussian Primes
THE MOAT PROBLEM. One cannot walk to infinity on the real line if one uses steps of bounded length and steps on the prime numbers. This is simply a restatement of the classic result that there are arbitrarily large gaps in the primes. The proof is simple: a gap of size k is given by (k + 1)! + 2, (k + 1)! + 3, ... (k + 1)! + (k + 1). But the same problem in the complex realm is unsolved. More p...
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We formulate Goldbach type questions for Gaussian, Hurwitz, Octavian and Eisenstein primes.
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Self-organizing maps are widely used in visual data mining. This paper proposes a new visualization approach for GHSOM algorithm, a hierarchical variant of SOM. The method is based on pie charts. That improves the visualization in hierarchical data structures making possible to extract all the existing relationships among the attributes of the neurons at any hierarchy level. The methodology is ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2021
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/haab009