Results 11 to 20 of about 19,257 (101)
Predicting Maximal Gaps in Sets of Primes
Mathematics, 2019 Let q > r ≥ 1 be coprime integers. Let P c = P c ( q , r , H ) be an increasing sequence of primes p satisfying two conditions: (i) p ≡ r (mod q) and (ii) p starts a prime k-tuple with a given pattern H ...
Alexei Kourbatov, Marek Wolf
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Artin's primitive root conjecture -a survey - [PDF]
, 2012 This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background.
Moree, Pieter
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, 2020 Our essays 1 to 11 describe the applicable Castell-Fact-Algorithm, which factorizes large integers, was ignored and rejected by economy and politics. Innovations concerning data protection and security seem not to be in great demand by neither the NSA, nor by Facebook & Co.
Tietken, Tom Hermann +1 more
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On primes in arithmetic progression having a prescribed primitive root. II
, 2007 Let a and f be coprime positive integers. Let g be an integer. Under the Generalized Riemann Hypothesis (GRH) it follows by a result of H.W. Lenstra that the set of primes p such that p=a(mod f) and g is a primitive root modulo p has a natural density ...
Moree, Pieter
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, 2007 We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$.
Davenport +6 more
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Laplacian Spectrum and Vertex Connectivity of the Unit Graph of the Ring \({ℤ_{p^{r}q^{s}}}\)
AxiomsIn this paper, we examine the interplay between the structural and spectral properties of the unit graph G(Zn) for n=p1r1p2r2…pkrk, where p1,p2,…,pk are distinct primes and k,r1,r2,…,rk are positive integers such that at least one of the ri must be ...
Amal Alsaluli +2 more
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Factorization of large tetra and penta prime numbers on IBM quantum processor
APL QuantumThe factorization of large digit integers in polynomial time is a challenging computational task to decipher. The development of Shor’s algorithm sparked a new resolution for solving the factorization problem.
Ritu Dhaulakhandi +2 more
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On the order of unimodular matrices modulo integers
, 2002 Assuming the Generalized Riemann Hypothesis, we prove the following: If b is an integer greater than one, then the multiplicative order of b modulo N is larger than N^(1-\epsilon) for all N in a density one subset of the integers.
Kurlberg, P.
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On Primes Represented by Quadratic Polynomials
, 2007 This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.Comment: six(6) pages, minor changes were ...
Baier, Stephan, Zhao, Liangyi
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The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequences [PDF]
, 2014 Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.Comment: 23 ...
Ballot, Christian
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