Erratum to “Analysis of Multiplication Tables by Sum, Difference and Product: A New Approach to Primality” [Advances in Pure Mathematics (2025) 505-517]
- 1 Independent Researcher, Conakry, Guinea
Abstract
The original online version of this article (Kadouno, G.J. (2025) Analysis of Multiplication Tables by Sum, Difference and Product: A New Approach to Primality. Advances in Pure Mathematics, 15, 505-517. https://doi.org/10.4236/apm.2025.158025 ) unfortunately contains mis-takes in the primality test (Sections 6-9). The author wishes to correct the scope of the primality claim, replace one numerical example, and restate the logarithmic version as a sieve with a proven performance guarantee. State-ments introduced in this erratum are labelled with the prefix E (Proposition E1, Theorem E1, ...) to distinguish them from those of the original article, to which we refer by their original numbers.
- Hardy, G.H. and Wright, E.M. (2008) An Introduction to the Theory of Numbers. 6th Edition, Oxford University Press, Oxford.
- Tenenbaum, G. (1995) Introduction to Analytic and Probabilistic Number Theory. Cambridge University Press, Cambridge.
- Mertens, F. (1874) Ein Beitrag zur analytischen Zahlentheorie. Journal fur die Reine und Angewandte Mathematik, 78, 46-62.
- Rabin, M.O. (1980) Probabilistic Algorithm for Testing Primality. Journal of Number Theory, 12, 128-138. https://doi.org/10.1016/0022-314x(80)90084-0
- Baillie, R. and Wagstaff, S.S. (1980) Lucas Pseudoprimes. Mathematics of Computation, 35, 1391-1417. https://doi.org/10.1090/s0025-5718-1980-0583518-6