• Corpus ID: 211043720

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

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