On prime k-tuples conjectures

V. Jotsov
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 2, Pages 39—44
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Authors and affiliations

V. Jotsov
Institute of Information Technologies of the Bulgarian Academy of Sciences
Acad. Bonchev Str. Bl. 29A, 1113 Sofia, Bulgaria


There exist cases when experiments with the computational part of the research could lead to new theoretical proofs. New hypotheses are suggested in concern with the Hardy–Littlewood conjecture that there exist infinitely many prime k-tuples. Although all the details on the presented investigation are given in another scope papers (applied mathematical logic), the formulation of the presented hypotheses has an independent role. Strong relations are revealed with the investigations from Number Theory period before the Hardy and Littlewood down to the Greek system. The introduced formulas help to establish upper and lower bounds for different constellations of prime k-tuples.


  • Elementary number theory
  • Hardy–Littlewood conjecture

AMS Classification

  • 11A05
  • 11A41


  1. K. Chandrasekharan, An Introduction to Analytic Number Theory, Springer- Verlag, Berlin, NY, 1968.
  2. P. Erdos and H. Riesel, On admissible constellations of consecutive primes. BIT 28 (1988) 391-396.
  3. H. Riesel, Prime Numbers and Computer Methods for Factorization, Birkhauser, Boston, 1985

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Cite this paper

Jotsov, V. (2000). On prime k-tuples conjectures. Notes on Number Theory and Discrete Mathematics, 6(2), 39-44.

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