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A classical problem in analytic number theory is to study the distribution of$\alpha p$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set ofprimes. We consider the subsequence generated by the primes $p$ such that $p+2$is an almost-prime (the existence of infinitely many such $p$ is anothertopical result in prime number theory) and prove that its distribution has asimilar property.

On the distribution of \alpha p modulo one for primes p of a special form