The Circle of Change

Sučić, Ines

doi:10.1002/9781119834175.ch1

Cited by 1 publication

(2 citation statements)

References 57 publications

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“…To illustrate this concept, let us consider the addition of elements from both infinite sets for various prime numbers ≥ 3 (although 2 is a prime number, we exempt it from each of the infinite sets since the addition of 2 to any prime number results to an odd number and not an even number). Therefore, the infinite set 𝑃 * is: 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53…”

Section: Construction Of the Proofmentioning

confidence: 99%

“…More recently, Daniel Sankei, Loyford Njagi, and Josephine Mutembei utilized a new formulation of even numbers [8] and the property that such even numbers can be partitioned into pairs of odd numbers [9] to numerically verify the Strong Goldbach Conjecture up to 9 × 10^18 [10]. In a more theoretical vein, Hardy and Littlewood made significant progress towards proving the conjecture in their groundbreaking work on the Hardy-Littlewood circle method [11].…”

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confidence: 99%

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A Detailed Proof of the Strong Goldbach Conjecture Based on Partitions of a New Formulation of a Set of Even Numbers

Sankei,

Njagi,

Mutembei

2024

ARJOM

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The Strong Goldbach's conjecture, a fundamental problem in Number Theory, asserts that every even integer greater than 2 can be expressed as the sum of two prime numbers. Despite significant efforts over centuries, this conjecture remains unproven, challenging the core of mathematics. The known algorithms for attempting to prove or verify the conjecture on a given interval [a,b] consist of finding two sets of primes Pi and Pj such that Pi+Pj cover all the even numbers in the interval [a,b]. However, the traditional definition of an even number as 2n for n ∈ ℕ (where ℕ is the set of natural numbers), has not provided mathematicians with a straightforward method to obtain all Goldbach partitions for any even number of this form. This paper introduces a novel approach to the problem, utilizing all odd partitions of an even number of a new formulation of the form Eij = ni + nj + (nj - ni)n or alln ∈ ℕ. By demonstrating that there exist at least a pair of prime numbers in these odd partitions, the fact that the sum of any two prime numbers is even and there exists infinitely many prime numbers, this paper provides a compelling proof of the conjecture. This breakthrough not only solves a long-standing mathematical mystery but also sheds light on the structure of prime numbers.

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