Abstract
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 m, every sufficiently large odd integer N can be written as a sum of three primes p1, p2 and p3 such that, for each i ϵ (1, 2, 3), the interval [pi, pi + H] contains at least m primes, for some H = H(m). Second, every sufficiently large integer N Ξ 3 (mod 6) can be written as a sum of three primes p1, p2 and p3 such that, for each i ϵ (1, 2, 3), pi + 2 has at most two prime factors.
Original language | English |
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Pages (from-to) | 1220-1256 |
Number of pages | 37 |
Journal | Compositio Mathematica |
Volume | 153 |
Issue number | 6 |
DOIs | |
State | Published - Jun 1 2017 |
Bibliographical note
Publisher Copyright:© Foundation Compositio Mathematica 2017.
Keywords
- Bohr sets
- Vinogradov's theorem
- sieve method
- transference principle
- twin primes
ASJC Scopus subject areas
- Algebra and Number Theory