Random Models for Artin Twin Primes

We say that a prime number p is an Artin prime for g if g is a primitive root mod p. For appropriately chosen integers g and d, we present a conjecture for the asymptotic number of prime pairs (p,p+d) such that both p and p+d are Artin primes for g. Our result suggests that the distribution of Artin prime pairs, amongst the ordinary prime pairs, is largely governed by a Poisson process. (Joint work with Magdaléna Tinková and Mikuláš Zindulka).

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