We are interested in classifying those sets of primes such that when we sieve out the integers up to by the primes in we are left with roughly the expected number of unsieved integers. In particular, we obtain the first general results for sieving an interval of length with primes including some in , using methods motivated by additive combinatorics.
"When the sieve works." Duke Math. J. 164 (10) 1935 - 1969, 15 July 2015. https://doi.org/10.1215/00127094-3120891