New evidence for the infinitude of some prime constellations

Thomas R. Nicely
Current e-mail address


A conjecture of Hardy and Littlewood, implying the twin-primes conjecture and featured in the work of Arenstorf, is extended to some other prime constellations. Computational evidence is presented in support of the conjectures, which imply the infinitude of these constellations, including the twin primes.


Primary: 11A41.
Secondary: 11N05, 11-04.


Prime constellations, twin-primes conjecture, prime triplets, prime quadruplets, prime k-tuples conjecture, Hardy-Littlewood approximations.


22 Oct  2004        Last modified.
20 July 2004        First posting.
15 July 2004        Rejected by Virginia Journal of Science.
12 July 2004        Revised version submitted to Virginia Journal of Science.
21 June 2004        Rejected by Journal of Integer Sequences.
19 June 2004        Submitted to Journal of Integer Sequences.

Copyright © 2004 Thomas R. Nicely. All rights reserved. This document may be reproduced and distributed for educational and non-profit purposes.