Bubbles of congruent primes

Details Bubbles of congruent primes Bubbles of congruent primes

2012-01-25

arxiv.org/abs/1201.5400v1

Mathematics

Number Theory

16 pages. A somewhat old paper, recently revised

Scientific paper

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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