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We record an implication between a recent result due to Li, Pratt and Shakan and large gaps between arithmetic progressions.
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Ford, K., Green, B., Konyagin, S., Maynard, J. and Tao, T., Long gaps between primes, J. Amer. Math. Soc., 31 (1) (2018), 65–105.
Ford, K., Green, B., Konyagin, S. and Tao, T., Large gaps between consecutive prime numbers, Ann. of Math., (2016), 935–974.
Kaptan, Deniz A. Large gaps between primes in arithmetic progressions, Not intended far publication, available at arXiv arXiv: 1809.09579, 2018.
Li, J., Pratt, K. and Shakan, G., A lower bound for the least prime in an arithmetic progression, Q. J. Math., 68 (3) (2017), 729–758.
Maynard, J. Large gaps between primes, Ann. of Math., 183 (3) (2016), 915–933.
Maynard, J., Small gaps between primes, Ann. of Math., (2015), 383–413.
Maynard, J., The twin prime conjecture, Japanese Journal of Mathematics, (2019), 1–32.
Pomerance, C., A note on the least prime in an arithmetic progression, J. Number Theory, 12 (2) (1980), 218–223.
Zaccagnini, A., A note on large gaps between consecutive primes in arithmetic progressions, J. Number Theory, 42 (1) (1992), 100–102.
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