On the sum of distinct primes or squares of primes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the sum of distinct primes or squares of primes

Authors:	Jin-Hui Fang Yong-Gao Chen

Institution:	1. Department of Mathematics, Nanjing University of Information Science & Technology, Nanjing 210044, PR China;2. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210046, PR China

Abstract:	In 1965 Erd?s introduced $f_{2} (s)$ : $f_{2} (s)$ is the smallest integer such that every $l > f_{2} (s)$ is the sum of s distinct primes or squares of primes where a prime and its square are not both used. We prove that for all sufficiently large s, $f_{2} (s) ? p_{2} + p_{3} + ? + p_{s + 1} + 3106$ , and the set of s with the equality has the density 1.

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