Artin prime producing quadratics

摘要

Fix an integerg. The primesp such thatg is a primitive root forp are calledArtin primes. Using a mixture of heuristics, well-known conjectures and rigorous arguments an algorithm is given to find quadratics that produce many Artin primes. Using this algorithmY. Gallot has found ag and a quadraticf such that the first 31082 primes produced byf haveg as a primitive root. There is a connection with finding integersd such thatL(2, (d/·)) is small.