Merge pull request #5 from kolosovpetro/MATH-100

MATH-100. Minimal Goldbach pairs in prime counting

Author: kolosovpetro

CHANGELOG.md

@@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning v2.0.0](https://semver.org/spec/v2.0.0.html).
 
+## [1.0.2] - 2025-04-20
+
+### Changed
+
+- Update abstract
+- Update readme
+
 ## [1.0.1] - 2025-04-20
 
 ### Changed

README.md

@@ -1,12 +1,10 @@
 # Minimal Goldbach pairs in prime and twin-prime counting
 
-Assuming Goldbach's Conjecture holds, every even integer $2N \geq 4$ can be written as $2N = p_i + p_j$
-where $(p_i, p_j)$ is called a Goldbach pair.
-
-The minimal Goldbach pair is a pair $(p_i,p_j)$ having the minimal $p_i$ such that $p_j = 2N - p_i$ is also a prime.
-
-We define a function $F_{2N}(P)$ that counts occurrences of $p_i = P$ within the range $6 \leq 2k \leq 2N$.
-
+Goldbach's Conjecture assumes that every even integer $2N \geq 4$ can be written as the sum of two primes
+$2N = p_i + p_j$, where $(p_i, p_j)$ is called a Goldbach pair.
+The minimal Goldbach pair is a pair $(p_i, p_j)$ such that $p_i$ is minimal and $p_j = 2N - p_i$ is also a prime.
+We define a function $F_{2N}(P)$ that counts the occurrences of $p_i = P$ within the range $6 \leq 2k \leq 2N$,
+where $P$ is a fixed prime number.
 In particular, the function $F_{2N}(P)$ provides the following identities in terms of prime counting $\pi(2N)$ and
 twin-prime counting $\pi_2(2N)$
 

out/MinimalGoldbachPairsInPrimesCounting.pdf

@@ -1,11 +1,10 @@
-Assuming Goldbach's Conjecture holds, every even integer $2N \geq 4 $ can be written as $2N = p_i + p_j$
-where $(p_i, p_j)$ is called a Goldbach pair.
-The minimal Goldbach pair is a pair $(p_i,p_j)$ having the minimal $p_i$ such that $p_j = 2N - p_i$ is also a prime.
-We define a function $F_{2N}(P)$ that counts occurrences of $p_i = P$ within the range $6 \leq 2k \leq 2N$,
-where $P$ is a prime.
+Goldbach's Conjecture assumes that every even integer $2N \geq 4$ can be written as the sum of two primes
+$2N = p_i + p_j$, where $(p_i, p_j)$ is called a Goldbach pair.
+The minimal Goldbach pair is a pair $(p_i, p_j)$ such that $p_i$ is minimal and $p_j = 2N - p_i$ is also a prime.
+We define a function $F_{2N}(P)$ that counts the occurrences of $p_i = P$ within the range $6 \leq 2k \leq 2N$,
+where $P$ is a fixed prime number.
 In particular, the function $F_{2N}(P)$ provides the following identities in terms of prime counting $\pi(2N)$ and
 twin-prime counting $\pi_2(2N)$
 \[
-    \pi(2N) = F_{2N+3}(3) + 1, \quad \pi_2(2N) = F_{2N+3}(3) - F_{2N+5}(5)
+    \pi(2N) = F_{2N+3}(3) + 1; \quad \pi_2(2N) = F_{2N+3}(3) - F_{2N+5}(5)
 \]
-