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16
Chains of large gaps between consecutive primes
 Adv. in Math
, 1981
"... ABSTRACT. Let G(x) denote the largest gap between consecutive grimes below x, In a series of papers from 1935 to 1963, Erdos, Rankin, and Schonhage showed that G(x):::: (c + o ( I)) logx loglogx log log log 10gx(loglog logx)2, where c = eY and y is Euler's constant. Here, this result is shown with ..."
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Cited by 11 (3 self)
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ABSTRACT. Let G(x) denote the largest gap between consecutive grimes below x, In a series of papers from 1935 to 1963, Erdos, Rankin, and Schonhage showed that G(x):::: (c + o ( I)) logx loglogx log log log 10gx(loglog logx)2, where c = eY and y is Euler's constant. Here, this result is shown with c = coe Y where Co = 1.31256... is the solution of the equation 4 / Co e4/co = 3. The principal new tool used is a result of independent interest, namely, a mean value theorem for generalized twin primes lying in a residue class with a large modulus. 1.
Integers represented as a sum of primes and powers of two
 Asian J. Math
"... It was shown by Linnik [10] that there is an absolute constant K such that every sufficiently large even integer can be written as a sum of two primes and at most ..."
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Cited by 9 (0 self)
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It was shown by Linnik [10] that there is an absolute constant K such that every sufficiently large even integer can be written as a sum of two primes and at most
On a diophantine problem with two primes and s powers of 2, Acta Arith
, 2010
"... We refine a recent result of Parsell [22] on the values of the form λ1p1+λ2p2+µ12 m1 ·· · + µs2 ms, where p1, p2 are prime numbers, m1,...,ms are positive integers, λ1/λ2 is negative and irrational and λ1/µ1, λ2/µ2 ∈ Q. ..."
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Cited by 7 (2 self)
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We refine a recent result of Parsell [22] on the values of the form λ1p1+λ2p2+µ12 m1 ·· · + µs2 ms, where p1, p2 are prime numbers, m1,...,ms are positive integers, λ1/λ2 is negative and irrational and λ1/µ1, λ2/µ2 ∈ Q.
An invitation to additive prime number theory
, 2004
"... The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sam ..."
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Cited by 4 (0 self)
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The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.
An upper bound in Goldbach's problem
 Math. Comp
, 1993
"... : It is clear that the number of distinct representations of a number n as the sum of two primes is at most the number of primes in the interval [n=2; n \Gamma 2]. We show that 210 is the largest value of n for which this upper bound is attained. 1. Introduction. In 1742 Christian Goldbach wrote, ..."
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Cited by 1 (1 self)
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: It is clear that the number of distinct representations of a number n as the sum of two primes is at most the number of primes in the interval [n=2; n \Gamma 2]. We show that 210 is the largest value of n for which this upper bound is attained. 1. Introduction. In 1742 Christian Goldbach wrote, in a letter to Euler, that on the evidence of extensive computations he was convinced that every integer exceeding 6 was the sum of three primes. Euler replied that if an even number 2n + 2 is so represented then one of those primes must be even and thus 2, so that every even number 2n, greater than 2, can be represented as the sum of two primes; it is easy to see that this conjecture implies Goldbach's original proposal, and it has widely become known as Goldbach's conjecture. Although still unresolved, Goldbach's conjecture is widely believed to be true. It has now been verified for every even integer up to 2 \Theta 10 10 (in [3]), and there are many interesting partial results worthy ...