Divisors of Shifted Primes

@article{Koukoulopoulos2010DivisorsOS,
  title={Divisors of Shifted Primes},
  author={Dimitris Koukoulopoulos},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2010},
  pages={4585-4627}
}
We bound from below the number of shifted primes p+s x that have a divisor in a given interval (y;z). Kevin Ford has obtained upper bounds of the expected order of magnitude on this quantity as well as lower bounds in a special case of the parameters y and z. We supply here the corresponding lower bounds in a broad range of the parameters y and z. As expected, these bounds depend heavily on our knowledge about primes in arithmetic progressions. As an application of these bounds, we determine… 
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