New quadratic polynomials with high densities of prime values

DOI10.1090/S0025-5718-02-01418-7zbMath1009.11060WikidataQ56095756 ScholiaQ56095756MaRDI QIDQ4780385

Michael J. Jacobson jun., Hugh C. Williams

Publication date: 19 November 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

class groupquadratic orderprime-generating quadratic polynomial

Mathematics Subject Classification ID

Quadratic extensions (11R11) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Polynomials (irreducibility, etc.) (11R09) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items (6)

New Computations Concerning the Cohen-Lenstra Heuristics ⋮ A lower bound for biases amongst products of two primes ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ The Bateman-Horn conjecture: heuristic, history, and applications ⋮ Artin prime producing quadratics ⋮ Artin prime producing polynomials

Uses Software

• LiDIA

Cites Work

• The size of \(L(1,\chi)\) for real nonpricipal residue characters \(\chi\) with prime modulus
• On the Conjecture of Hardy & Littlewood concerning the Number of Primes of the Form n 2 + a
• Quadratic Polynomials which have a High Density of Prime Values
• A Rigorous Subexponential Algorithm For Computation of Class Groups
• The Multiple Polynomial Quadratic Sieve
• A Probabilistic Factorization Algorithm with Quadratic Forms of Negative Discriminant
• Integer Sequence having Prescribed Quadratic Character
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