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arXiv · 1201.5400

Bubbles of congruent primes

Frank Thorne
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Abstract

Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu's theorem to imaginary quadratic fields, where we prove the existence of "bubbles" containing arbitrarily many primes which are all, up to units, congruent to a modulo q.

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Frank Thorne. 2012-01-25. Bubbles of congruent primes. https://doi.org/10.1017/s0305004114000425

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