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This paper presents evidence of a recursive fractal structure in the distribution of prime numbers,revealed through triplet decomposition and recursive extraction of strings based on the position of primeswithin triplets. Each level of recursion yields three new strings (X, Y, Z), forming a tree-like topology ofprime-derived sequences.
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This paper presents evidence of a recursive fractal structure in the distribution of prime numbers,revealed through triplet decomposition and recursive extraction of strings based on the position of primeswithin triplets. Each level of recursion yields three new strings (X, Y, Z), forming a tree-like topology ofprime-derived sequences.
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Canadian Journal of Mathematics, 1995
AbstractAn additive subgroupPof a skew fieldFis called aprimeofFifPdoes not contain the identity, but if the productxyof two elementsxandyinFis contained inP, thenxoryis inP. A prime segment ofFis given by two neighbouring primesP1⊃P2; such a segment is invariant, simple, or exceptional depending on whetherA(P1) = {a∈P1|P1aP1⊂P1} equalsP1,P2or lies ...
Brungs, H. H., Schröder, M.
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AbstractAn additive subgroupPof a skew fieldFis called aprimeofFifPdoes not contain the identity, but if the productxyof two elementsxandyinFis contained inP, thenxoryis inP. A prime segment ofFis given by two neighbouring primesP1⊃P2; such a segment is invariant, simple, or exceptional depending on whetherA(P1) = {a∈P1|P1aP1⊂P1} equalsP1,P2or lies ...
Brungs, H. H., Schröder, M.
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Testing Low-Degree Polynomials over Prime Fields
45th Annual IEEE Symposium on Foundations of Computer Science, 2004AbstractWe present an efficient randomized algorithm to test if a given functionf: 𝔽→ 𝔽p(wherepis a prime) is a low‐degree polynomial. This gives a local test for Generalized Reed‐Muller codes over prime fields. For a given integertand a given real ε > 0, the algorithm queriesfatO($ O({{1}\over{\epsilon}}+t.p^{{2t \over p-1}+1}) $) points to ...
Jutla, Charanjit S. +3 more
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Normal Rational Curves Over Prime Fields
Designs, Codes and Cryptography, 1997A \(k\)-arc of \(PG(n,q)\), with \(k \geq n+1\), is set of \(k\) points of \(PG(n,q)\) such that no \(n+1\) of them belong to a hyperplane. Standard examples of \((q+1)\)-arcs of \(PG(n,q)\) are the normal rational curves. The author characterizes the normal rational curves in \(PG(n,p)\) for \(p\) prime and \(2 \leq n \leq p-2\) as the only \((p+1 ...
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Prime Tuples in Function Fields
2016How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future.
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Affine extractors over prime fields
Combinatorica, 2011An affine extractor is a map from the \(n\)-dimensional vector space over a finite field to the field that is balanced on every affine subspace of sufficiently large dimension. Affine extractors have been studied by \textit{A.~Gabizon} and \textit{R.~Raz} [Combinatorica 28, No.
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Kummer for Genus One Over Prime-Order Fields
Journal of Cryptology, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karati, Sabyasachi, Sarkar, Palash
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