An approximation to the twin prime conjecture and the parity phenomenon
نویسندگان
چکیده
منابع مشابه
An Introduction to The Twin Prime Conjecture
Twin primes are primes of the form (p, p + 2). There are many proofs for the infinitude of prime numbers, but it is very difficult to prove whether there are an infinite number of pairs of twin primes. Most mathemati cians agree that the evidence points toward this conclusion, but numerous attempts at a proof have been falsified by subsequent review. The prob lem itself, one of the most famou...
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For every even integerN , denote byD(N) andD1,2(N) the number of representations of N as a sum of two primes and as a sum of a prime and an integer having at most two prime factors, respectively. In this paper, we give a new upper bound for D(N) and a new lower bound for D1,2(N), which improve the corresponding results of Chen. We also obtain similar results for the twin prime problem
متن کاملAverage Twin Prime Conjecture for Elliptic Curves
Let E be an elliptic curve over 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 Fp is prime. This is an analogue of the Hardy–Littlewood twin prime conjecture in the case of elliptic curves. Koblitz’s Conjecture is still widely open. In this paper we prove that Koblitz’s Conjecture is true on average...
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In this paper we use the connected sum operation on knots to show that there is a one-to-one relation between knots and numbers. In this relation prime knots are bijectively assigned with prime numbers such that the prime number 2 corresponds to the trefoil knot. From this relation we have a classification table of knots where knots are one-to-one assigned with numbers. Further this assignment ...
متن کاملA Polynomial Analogue of the Twin Prime Conjecture
We consider the problem of counting the number of (not necessarily monic) ‘twin prime pairs’ P, P + M ∈ Fq [T ] of degree n, where M is a polynomial of degree < n. We formulate an asymptotic prediction for the number of such pairs as qn → ∞ and then prove an explicit estimate confirming the conjecture in those cases where q is large compared with n2. When M has degree n− 1, our theorem implies ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2015
ISSN: 0019-3577
DOI: 10.1016/j.indag.2015.09.008