The Difference Between Consecutive Primes, II
نویسندگان
چکیده
منابع مشابه
The Difference between Consecutive Primes, Ii
With enough effort, the value of x0 could be determined effectively. The paper has much in common with [1]; in particular we use the sieve method of Harman [4, 5]. We no longer use zero density estimates, however, but rather mean value results on Dirichlet polynomials similar to those that give rise to such estimates. Compare, for example, work of Iwaniec and Pintz [9] and Baker, Harman and Pin...
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is greater than (c2/2)n. A simple calculation now shows that the primes satisfying (4) also satisfy the first inequality of (3) i΀ = e(ci) is chosen small enough. The second inequality of (3) is proved in the same way, which proves Theorem 2. Further, we obtain, as an immediate corollary of Theorem 1, that Received by the editors October 17, 1947. 1 P. Erdös and P. Turân, Some new questions on...
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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 = coeY where Co = 1.31256... is the solution of the equation 4/ Co e -4/co = 3 . The principal new tool ...
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For any real x, the most common difference that occurs among the consecutive primes less than or equal to x is called a jumping champion. This term was introduced by J. H. Conway in 1993. There are occasionally ties. Therefore there can be more than one jumping champion for a given x. The first, but short-lived, jumping champion is 1. Aside from the numerical studies, nothing else has been prov...
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It is shown that the classical Ramsey numbers T( m, ta) satisfy r(m,n) 2: r(m,n1) + 2m3,
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2001
ISSN: 0024-6115
DOI: 10.1112/plms/83.3.532