Results 11 to 20 of about 15,692 (133)
Average twin prime conjecture for elliptic curves [PDF]
American Journal of Mathematics, 2011 Let $E$ be an elliptic curve over ${\Bbb Q}$. In 1988, N. Koblitz conjectured a precise asymptotic for the number of primes $p$ up to $x$ such that the order of the group of points of $E$ over ${\Bbb F}_p$ is prime. This is an analogue of the Hardy--Littlewood twin prime conjecture in the case of elliptic curves Koblitz's conjecture ...
Balog, A., Cojocaru, A., David, C.
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Conjecture of twin primes (Still unsolved problem in Number Theory). An expository essay [PDF]
Surveys in Mathematics and its Applications, 2017 The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes ...
Hayat Rezgui
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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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Twin Prime Conjecture - Proof that there are infinite twin primes. [PDF]
, 2021 We determine that twin primes are not random within specific range of number series. Within the range, they are part of an infinite repeating cycle within the series. The repeating cycles of this series is symmetrical and that range is part of one such cycle. We can also determine where in the repeating cycle this range is located.
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, 2023 Abstract The Twin Prime conjecture first proposed by French mathematician Alphonse de Polignac in the year 1846 remains unproven until now. This paper sets out to prove the Twin Prime conjecture by creating a system of equations and finding both a y element of ℕ, (y ϵ ℕ) and a y element of k, (y ϵ k) to find the twin prime values and ...
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Siegel Zeros, Twin Primes, Goldbach’s Conjecture, and Primes in Short Intervals
International Mathematics Research Notices, 2023 Abstract We study the distribution of prime numbers under the unlikely assumption that Siegel zeros exist. In particular, we prove for $$ \begin{align*} & \sum_{n \leq X} \Lambda(n) \Lambda(\pm n+h) \end{align*}$$an asymptotic formula that holds uniformly for $h = O(X)$.
Matomäki Kaisa, Merikoski Jori
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On the numbers that determine the distribution of twin primes [PDF]
Surveys in Mathematics and its Applications, 2018 This paper is about a class of numbers indirectly connected to the twin primes, which have not been investigated so far. With the help of these numbers, we look at the set of twin primes from a different perspective and bring the reader's attention to ...
Antonie Dinculescu
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Japanese Journal of Mathematics, 2019 In the last fifteen years or so there has been a wealth of results and methods dealing with small differences between primes (in what follows \(p\) with or without subscripts denotes primes). The author of this impressive overview paper is one of the mathematicians who has made some of the most important contributions in this field.
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Proof for Twin Prime Conjecture
, 2023 "Twin primes are prime numbers that differ by 2. Are there infinitely many twin primes?"
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