Artin prime producing quadratics
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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.
2000 Mathematics Subject Classification11Y55 11A07 11B83
- H. Cohen, High precision computation of Hardy-Littlewood constants. Draft of a preprint (see his homepage).Google Scholar
- K. Ireland andM. Rosen,A classical introduction to modern number theory. 2nd ed., Graduate Texts in Mathematics84, Springer-Verlag, New York, 1990.Google Scholar
- P. Moree, Problem 1097.Elem. Math. 50 (1995), p. 82. (Solution 51 (1996), 81–82.)Google Scholar
- S. C. van Veen, Probability problems in throwing dice. (Dutch),Nieuw Arch. Wiskunde 17 (1932), 120–136, 209–239.Google Scholar