A1 Refereed original research article in a scientific journal
Vinogradov's three primes theorem with almost twin primes
Authors: Kaisa Matomäki, Xuancheng Shao
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2017
Journal: Compositio Mathematica
Journal name in source: COMPOSITIO MATHEMATICA
Journal acronym: COMPOS MATH
Volume: 153
Issue: 6
First page : 1220
Last page: 1256
Number of pages: 37
ISSN: 0010-437X
eISSN: 1570-5846
DOI: https://doi.org/10.1112/S0010437X17007072
Web address : https://www.cambridge.org/core/journals/compositio-mathematica/article/vinogradovs-three-primes-theorem-with-almost-twin-primes/F9F16D0810AD32E055BC1002C35CBE05
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/20698389
In this paper we prove two results concerning Vinogradov's three primes theorem with primes that can be called almost twin primes. First, for any in, every sufficiently large odd integer N can be written as a sum of three primes p(1), p(2) and p(3) such that, for each i is an element of {1, 2, 3}, the interval [p(i), p(i) + H] contains at least m, primes, for some H = H (m). Second, every sufficiently large integer N 3 (mod 6) can be written as a sum of three primes p(1), p(2) and p(3) such that, for each i is an element of {1, 2, 3}, p(i) + 2 has at most two prime factors.
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