# On the first occurrences of gaps between primes in a residue class

@article{Kourbatov2020OnTF, title={On the first occurrences of gaps between primes in a residue class}, author={Alexei Kourbatov and Marek Wolf}, journal={arXiv: Number Theory}, year={2020} }

We study the first occurrences of gaps between primes in the arithmetic progression (P): $r$, $r+q$, $r+2q$, $r+3q,\ldots,$ where $q$ and $r$ are coprime integers, $q>r\ge1$. The growth trend and distribution of the first-occurrence gap sizes are similar to those of maximal gaps between primes in (P). The histograms of first-occurrence gap sizes, after appropriate rescaling, are well approximated by the Gumbel extreme value distribution. Computations suggest that first-occurrence gaps are much…

## One Citation

Large gaps between primes in arithmetic progressions -- an empirical approach

- Mathematics
- 2022

An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in…

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