**Shiu's theorem**: for any $k \geq 1$ and $(a, q) = 1$ there exist infinitely many $k$-tuples of consecutive primes
$p_m, \dots, p_{m + k - 1}$ all of which are congruent to $a$ modulo $q$.
[Sh00] Shiu, D. K. L., _Strings of congruent primes_. J. London Math. Soc. (2) (2000), 359-373.
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