Primes in tuples IV: Density of small gaps between consecutive primes
نویسندگان
چکیده
منابع مشابه
Small Gaps between Primes or Almost Primes
Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that lim inf n→∞ (pn+1 − pn) log pn = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let qn denote the nth number that is a product of exactly two distinct primes. We prove that lim inf n→∞ (qn+1 − qn) ≤ 26. If an appropriate generalization of ...
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Finding mathematical proofs for easily observed properties of the distribution of prime numbers is a difficult and often humbling task, at least for the authors of this paper. The twin prime conjecture is a famous example of this, but we are concerned here with the much more modest problem of proving that there are arbitrarily large primes that are “unusually close ” together. Statistically thi...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2013
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa160-1-3