New evidence for the infinitude of some prime constellations
Thomas R. Nicely
ABSTRACT
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.
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MATHEMATICS SUBJECT CLASSIFICATION (MSC2000)
Primary: 11A41.
Secondary: 11N05, 11-04.
KEYWORDS
Prime constellations, twin-primes conjecture, prime triplets,
prime quadruplets, prime k-tuples conjecture, Hardy-Littlewood
approximations.
DOCUMENT HISTORY
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.
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