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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

A recursion relation for the number of Goldbach partitions of an even integer

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pp. 1–30Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1188 Crossmark XML
Received:
08 Apr 2020
Published Online:
24 Jan 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1188
Pages:
1–30

Abstract

The contour integral representation of the number of Goldbach partitions of an even integer, G(n), is extended to an integral with a support function that equals a linear combination of integers {G(m)}. A support function is found such that there is a nontrivial integral relation relating number of Goldbach partitions of n and m < n. The proof of the existence of a partition of any even integer greater than or equal to four into the sum of two primes follows from a recursion relation, resulting from an integral identity, that yields a non-zero lower bound for G(n). A partition of n, given a partition of n/2 , is derived from an algorithm based on solutions to congruence relations related to the roots of unity. This result provides a method for generating a prime partition of every even integer greater than or equal to 6 in addition to the above demonstration of its existence.

Keywords

Goldbach partitionCauchy integral

Subject Classifications

11P3230E20

References

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