Primes in tuples I
Primes in tuples I
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DOI：
10.4007/annals.2009.170.819
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发表时间：
2005-08
影响因子：
4.9
通讯作者：
D. Goldston;J. Pintz;C. Yıldırım
中科院分区：
文献类型：
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作者：
D. Goldston;J. Pintz;C. Yıldırım
我们介绍一种方法来证明存在非常接近的素数。该方法取决于算术级数中素数的分布水平。假设 Elliott-Halberstam 猜想，我们证明存在无数个相差 16 或更小的素数。即使是一个弱得多的猜想也意味着，间隔有界距离的素数常常是无限的。我们无条件地证明存在比平均间距的任意小倍数更接近的连续素数，即 lim inf n→∞ Pn+1-Pn/log Pn/log = 0。我们将在后面的论文中进一步量化这个结果。
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance apart. Unconditionally, we prove that there exist consecutive primes which are closer than any arbitrarily small multiple of the average spacing, that is, lim inf n→∞ Pn+1-Pn/log Pn/log = 0. We will quantify this result further in a later paper.