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.
|Number of pages||37|
|State||Published - Jun 1 2017|
Bibliographical notePublisher Copyright:
© Foundation Compositio Mathematica 2017.
- Bohr sets
- Vinogradov's theorem
- sieve method
- transference principle
- twin primes
ASJC Scopus subject areas
- Algebra and Number Theory