@article{Erdos1962,
  author = {Erd{\H{o}}s, P.},
  title = {On the integers relatively prime to {$n$} and on a number-theoretic
           function considered by {Jacobsthal}},
  journal = {Mathematica Scandinavica},
  volume = {10},
  year = {1962},
  pages = {163--170},
  doi = {10.7146/math.scand.a-10523},
  url = {https://journals.msp.org/mscand/article/view/2667},
  note = {\url{https://doi.org/10.7146/math.scand.a-10523}}
}

@article{Iwaniec1978,
  author = {Iwaniec, Henryk},
  title = {On the problem of {Jacobsthal}},
  journal = {Demonstratio Mathematica},
  volume = {11},
  number = {1},
  year = {1978},
  pages = {225--231},
  doi = {10.1515/dema-1978-0121},
  url = {https://www.degruyterbrill.com/document/doi/10.1515/dema-1978-0121/html},
  note = {\url{https://doi.org/10.1515/dema-1978-0121}}
}

@article{HajduSaradha2012,
  author = {Hajdu, L. and Saradha, N.},
  title = {Disproof of a conjecture of {Jacobsthal}},
  journal = {Mathematics of Computation},
  volume = {81},
  number = {280},
  year = {2012},
  pages = {2461--2471},
  doi = {10.1090/S0025-5718-2012-02581-6},
  url = {https://math.unideb.hu/sites/default/files/inline-files/jacobsrevsaradha.pdf},
  note = {\url{https://doi.org/10.1090/S0025-5718-2012-02581-6}}
}

@book{FriedlanderIwaniec2010,
  author = {Friedlander, John and Iwaniec, Henryk},
  title = {Opera de Cribro},
  series = {American Mathematical Society Colloquium Publications},
  volume = {57},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2010},
  doi = {10.1090/coll/057},
  url = {https://bookstore.ams.org/COLL/57},
  note = {\url{https://doi.org/10.1090/coll/057}}
}

@article{Sofos2023,
  author = {Sofos, Efthymios},
  title = {Gaps between prime divisors and analogues in {Diophantine} geometry},
  journal = {Glasgow Mathematical Journal},
  volume = {65},
  number = {S1},
  pages = {S129--S147},
  year = {2023},
  doi = {10.1017/S0017089522000398},
  url = {https://doi.org/10.1017/S0017089522000398},
  note = {\url{https://doi.org/10.1017/S0017089522000398}}
}

@article{MontgomeryVaughan1973,
  author = {Montgomery, H. L. and Vaughan, R. C.},
  title = {The large sieve},
  journal = {Mathematika},
  volume = {20},
  number = {2},
  pages = {119--134},
  year = {1973},
  doi = {10.1112/S0025579300004708},
  url = {https://doi.org/10.1112/S0025579300004708},
  note = {\url{https://doi.org/10.1112/S0025579300004708}}
}

@misc{VaughanLargeSieve,
  author = {Vaughan, Robert C.},
  title = {{Math 571}, Chapter 5: The large sieve},
  year = {2025},
  month = feb,
  howpublished = {Lecture notes},
  url = {https://personal.science.psu.edu/rcv4/571s25/Class571-05.pdf},
  note = {Dated February 20, 2025.
          \url{https://personal.science.psu.edu/rcv4/571s25/Class571-05.pdf}}
}

@book{IwaniecKowalski2004,
  author = {Iwaniec, Henryk and Kowalski, Emmanuel},
  title = {Analytic Number Theory},
  series = {American Mathematical Society Colloquium Publications},
  volume = {53},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2004},
  doi = {10.1090/coll/053},
  url = {https://bookstore.ams.org/COLL/53},
  note = {\url{https://doi.org/10.1090/coll/053}}
}

@misc{Lichtman2022,
  author = {Lichtman, Jared Duker},
  title = {Primes in arithmetic progressions to large moduli, and shifted
           primes without large prime factors},
  year = {2022},
  howpublished = {Preprint, arXiv:2211.09641v1},
  eprint = {2211.09641v1},
  archivePrefix = {arXiv},
  primaryClass = {math.NT},
  url = {https://arxiv.org/abs/2211.09641v1},
  note = {\url{https://arxiv.org/abs/2211.09641v1}}
}

@article{Estermann1961,
  author = {Estermann, T.},
  title = {On {Kloosterman}'s sum},
  journal = {Mathematika},
  volume = {8},
  number = {1},
  pages = {83--86},
  year = {1961},
  doi = {10.1112/S0025579300002187},
  url = {https://doi.org/10.1112/S0025579300002187},
  note = {\url{https://doi.org/10.1112/S0025579300002187}}
}

@article{Huxley1972,
  author = {Huxley, M. N.},
  title = {On the difference between consecutive primes},
  journal = {Inventiones Mathematicae},
  volume = {15},
  number = {2},
  pages = {164--170},
  year = {1972},
  doi = {10.1007/BF01418933},
  url = {https://link.springer.com/article/10.1007/BF01418933},
  note = {\url{https://doi.org/10.1007/BF01418933}}
}

@article{HeathBrown1982,
  author = {Heath-Brown, D. R.},
  title = {Prime numbers in short intervals and a generalized {Vaughan} identity},
  journal = {Canadian Journal of Mathematics},
  volume = {34},
  number = {6},
  pages = {1365--1377},
  year = {1982},
  doi = {10.4153/CJM-1982-095-9},
  url = {https://doi.org/10.4153/CJM-1982-095-9},
  note = {\url{https://doi.org/10.4153/CJM-1982-095-9}}
}

@misc{GranvilleSoundararajan,
  author = {Granville, Andrew and Soundararajan, K.},
  title = {The distribution of prime numbers},
  howpublished = {Undated draft},
  url = {https://dms.umontreal.ca/~andrew/PDF/PretendBook050111.pdf},
  note = {\url{https://dms.umontreal.ca/~andrew/PDF/PretendBook050111.pdf}.
          Accessed September 25, 2026}
}

@misc{GranvilleSoundararajan2014,
  author = {Granville, Andrew and Soundararajan, K.},
  title = {Multiplicative number theory: The pretentious approach},
  year = {2014},
  howpublished = {Draft},
  url = {https://dms.umontreal.ca/~andrew/PDF/Book.To2.5.pdf},
  note = {\url{https://dms.umontreal.ca/~andrew/PDF/Book.To2.5.pdf}}
}

@misc{MontgomeryVaughanIII,
  author = {Montgomery, Hugh L. and Vaughan, Robert C.},
  title = {Multiplicative Number Theory {III}},
  howpublished = {Undated draft},
  url = {https://personal.science.psu.edu/rcv4/571s25/Vol3.pdf},
  note = {\url{https://personal.science.psu.edu/rcv4/571s25/Vol3.pdf}.
          Accessed September 25, 2026}
}

@book{Serfozo2009,
  author = {Serfozo, Richard},
  title = {Basics of Applied Stochastic Processes},
  series = {Probability and Its Applications},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {2009},
  doi = {10.1007/978-3-540-89332-5},
  url = {https://link.springer.com/book/10.1007/978-3-540-89332-5},
  note = {\url{https://doi.org/10.1007/978-3-540-89332-5}}
}

@article{FioriKadiriSwidinsky2023,
  author = {Fiori, Andrew and Kadiri, Habiba and Swidinsky, Joshua},
  title = {Sharper bounds for the error term in the prime number theorem},
  journal = {Research in Number Theory},
  volume = {9},
  number = {3},
  year = {2023},
  eid = {63},
  doi = {10.1007/s40993-023-00454-w},
  url = {https://link.springer.com/article/10.1007/s40993-023-00454-w},
  note = {Article 63.
          \url{https://doi.org/10.1007/s40993-023-00454-w}.
          Author version \url{https://arxiv.org/abs/2206.12557v2}}
}

@misc{Tao2015Sieve,
  author = {Tao, Terence},
  title = {{254A}, Notes 4: Some sieve theory},
  year = {2015},
  month = jan,
  howpublished = {Author's course notes},
  url = {https://terrytao.wordpress.com/2015/01/21/254a-notes-4-some-sieve-theory/},
  note = {\url{https://terrytao.wordpress.com/2015/01/21/254a-notes-4-some-sieve-theory/}}
}

@article{Vaughan1977,
  author = {Vaughan, R. C.},
  title = {On the order of magnitude of {Jacobsthal}'s function},
  journal = {Proceedings of the Edinburgh Mathematical Society},
  volume = {20},
  number = {4},
  year = {1977},
  pages = {329--331},
  doi = {10.1017/S0013091500026560},
  note = {\url{https://doi.org/10.1017/S0013091500026560}}
}

@article{BanksFordTao2023,
  author = {Banks, William and Ford, Kevin and Tao, Terence},
  title = {Large prime gaps and probabilistic models},
  journal = {Inventiones Mathematicae},
  volume = {233},
  number = {3},
  year = {2023},
  pages = {1471--1518},
  doi = {10.1007/s00222-023-01199-0},
  note = {Corrected version: arXiv:1908.08613v3 (2025).
          \url{https://arxiv.org/abs/1908.08613v3}}
}

@article{Gallagher1976,
  author = {Gallagher, P. X.},
  title = {On the distribution of primes in short intervals},
  journal = {Mathematika},
  volume = {23},
  number = {1},
  year = {1976},
  pages = {4--9},
  doi = {10.1112/S0025579300016442},
  note = {\url{https://doi.org/10.1112/S0025579300016442}}
}

@article{FGKMT2018,
  author = {Ford, Kevin and Green, Ben and Konyagin, Sergei and
            Maynard, James and Tao, Terence},
  title = {Long gaps between primes},
  journal = {Journal of the American Mathematical Society},
  volume = {31},
  number = {1},
  year = {2018},
  pages = {65--105},
  doi = {10.1090/jams/876},
  note = {\url{https://doi.org/10.1090/jams/876}}
}

@article{CostelloWatts2015,
  author = {Costello, Fintan and Watts, Paul},
  title = {An upper bound on {Jacobsthal}'s function},
  journal = {Mathematics of Computation},
  volume = {84},
  number = {293},
  year = {2015},
  pages = {1389--1399},
  doi = {10.1090/S0025-5718-2014-02896-2},
  note = {\url{https://doi.org/10.1090/S0025-5718-2014-02896-2}}
}

@misc{Ziller2019,
  author = {Ziller, Mario},
  title = {New computational results on a conjecture of {Jacobsthal}},
  year = {2019},
  howpublished = {Preprint, arXiv:1903.11973v2},
  note = {\url{https://arxiv.org/abs/1903.11973v2}}
}

@article{Jarnik1926,
  author = {Jarn{\'i}k, Vojt{\v e}ch},
  title = {{\"U}ber die {Gitterpunkte} auf konvexen {Kurven}},
  journal = {Mathematische Zeitschrift},
  volume = {24},
  year = {1926},
  pages = {500--518},
  url = {https://dml.cz/handle/10338.dmlcz/500690},
  note = {\url{https://dml.cz/handle/10338.dmlcz/500690}}
}

@incollection{HelfgottVenkatesh2009,
  author = {Helfgott, H. A. and Venkatesh, A.},
  title = {How small must ill-distributed sets be?},
  booktitle = {Analytic Number Theory: Essays in Honour of {Klaus Roth}},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {2009},
  pages = {224--234},
  url = {https://webusers.imj-prg.fr/~harald.helfgott/texts/howsmall.pdf},
  note = {\url{https://webusers.imj-prg.fr/~harald.helfgott/texts/howsmall.pdf}}
}

@article{Walsh2012,
  author = {Walsh, Miguel N.},
  title = {The inverse sieve problem in high dimensions},
  journal = {Duke Mathematical Journal},
  volume = {161},
  number = {10},
  year = {2012},
  pages = {2001--2022},
  doi = {10.1215/00127094-1645788},
  url = {https://arxiv.org/abs/1105.1551v2},
  note = {\url{https://doi.org/10.1215/00127094-1645788};
          author version \url{https://arxiv.org/abs/1105.1551v2}}
}

@misc{MontgomeryVaughanII,
  author = {Montgomery, Hugh L. and Vaughan, Robert C.},
  title = {Multiplicative Number Theory {II}: Primes and Sieves},
  howpublished = {Undated author draft},
  url = {https://personal.science.psu.edu/rcv4/571s25/montgomery-vaughanII.pdf},
  note = {\url{https://personal.science.psu.edu/rcv4/571s25/montgomery-vaughanII.pdf}.
          Accessed September 25, 2026}
}

@article{Gallagher1971,
  author = {Gallagher, P. X.},
  title = {A larger sieve},
  journal = {Acta Arithmetica},
  volume = {18},
  year = {1971},
  pages = {77--81},
  doi = {10.4064/aa-18-1-77-81},
  note = {\url{https://doi.org/10.4064/aa-18-1-77-81}}
}

@article{Jacobsthal1960,
  author = {Jacobsthal, Ernst},
  title = {{\"U}ber {Sequenzen} ganzer {Zahlen}, von denen keine zu {$n$}
           teilerfremd ist. {I--III}},
  journal = {Norske Vidensk. Selsk. Forh. Trondheim},
  volume = {33},
  year = {1960},
  pages = {117--139}
}

@article{Iwaniec1971,
  author = {Iwaniec, Henryk},
  title = {On the error term in the linear sieve},
  journal = {Acta Arithmetica},
  volume = {19},
  number = {1},
  year = {1971},
  pages = {1--30},
  doi = {10.4064/aa-19-1-1-30},
  note = {\url{https://doi.org/10.4064/aa-19-1-1-30}}
}

@article{Walsh2014,
  author = {Walsh, Miguel N.},
  title = {The algebraicity of ill-distributed sets},
  journal = {Geometric and Functional Analysis},
  volume = {24},
  number = {3},
  year = {2014},
  pages = {959--967},
  note = {\url{https://arxiv.org/abs/1307.0259}}
}