Vinogradov's three primes theorem with almost twin primes
CAMBRIDGE UNIV PRESS
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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.