Large gaps between consecutive prime numbers containing perfect k-th powers of prime numbers

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• 作者：Helmut Maier^a ; ^{helmut.maier@uni-ulm.de} ; Michael Th. Rassias^b ; ^c ; ^{michail.rassias@math.uzh.ch} ; ^{michailrassias@math.princeton.edu}
• 关键词：Gaps of primes ; Sieve estimate ; Covering theorem ; Arithmetic progression ; Probabilistic covering ; Uniform covering ; Chebyshev's inequality
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：272
• 期：6
• 页码：2659-2696
• 全文大小：517 K
• 卷排序：272

文摘

Let k≥2k≥2 be a fixed natural number. We establish the existence of infinitely many pairs of consecutive primes pnpn, pn+1pn+1 satisfyingpn+1−pn≥clog⁡pnlog2⁡pnlog4⁡pnlog3⁡pn, with c   being a fixed positive constant, for which the interval (pn,pn+1)(pn,pn+1) contains the k-th power of a prime number.