The Difference Between Consecutive Primes
The Difference Between Consecutive Primes
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DOI：
10.1112/plms/s3-72.2.261
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发表时间：
1996-03
影响因子：
1.8
通讯作者：
R. Baker;G. Harman
中科院分区：
文献类型：
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作者：
R. Baker;G. Harman
定理1。对于所有大的x，区间[x-x'535， x]包含素数。只要付出足够的努力，就可以有效地确定一个值x0，使结果对x> x0保持不变；我们不讨论这件事的细节。这个问题起源于一个经典的猜想，即在连续的平方之间存在一个素数。自从Hoheisel[7]给出了第一个非平凡的结果以来，许多作者都在考虑这个问题。在筛分法应用于该问题之前获得的最佳结果是由于赫胥黎[8]（对于任意e[8]，其指数为ft+£）。筛法最早由Iwaniec和Jutila[6]（指数9）成功引入该地区，Heath-Brown和Iwaniec[6]（指数9）对筛法进行了改进。随后Iwaniec和Pintz[12]以及Mozzochi[12]对其进行了小的改进。最近Lou和Yao将指数提高到ft b[13]，并声称ft可以通过他们的方法在经过艰苦的计算后获得。为了方便读者，我们注意到这一点
THEOREM 1. For all large x, the interval [x-x'535, x] contains prime numbers.With enough effort, one could effectively determine a value x0 such that the result holds for x> x0; we shall not discuss the details of this. This problem, which has its genesis in the classical conjecture that there is a prime between consecutive squares, has been considered by many authors since the first non-trivial result was given by Hoheisel [7]. The best result which was obtained before sieve methods were applied to the problem is due to Huxley [8](with exponent ft+£, for any e> 0). A sieve method was first successfully introduced into this area by Iwaniec and Jutila [11](exponent 9) and refined by Heath-Brown and Iwaniec [6](^). Small improvements were subsequently made by Iwaniec and Pintz [12] and Mozzochi [15]. Recently Lou and Yao have improved the exponent to ft [13] and claim that ft is accessible by their methods after arduous calculations. For the convenience of the reader we note that