Abstrakt
We say that a prime number p is an Artin prime for g if g mod p generates the group (Z/pZ)x. For appropriately chosen integers d and g, we present a conjecture for the asymptotic number 7rd,g(x) of primes p <= x such that both p and p + d are Artin primes for g.
In particular, we identify a class of pairs (d, g) for which 7rd,g(x) = 0. Our results suggest that the distribution of Artin prime pairs, amongst the ordinary prime pairs, is largely governed by a Poisson binomial distribution.(c) 2022 Elsevier Inc.
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