Let m be a natural number, and let Q be a set containing at least exp(Cm) primes. We show that one can find infinitely many strings of m consecutive primes each of which has some q ∈ Q as a primitive root, all lying in an interval of length OQ(exp(C ′m)). This is a bounded gaps variant of a theorem of Gupta and Ram Murty. We also prove a result on an… (More)
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