Merge pull request #4 from kolosovpetro/MATH-100

MATH-100. Minimal Goldbach pairs in prime counting

Author: kolosovpetro

CHANGELOG.md

@@ -5,7 +5,14 @@ All notable changes to this project will be documented in this file.
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-## [1.0.0] - 2025-04-19
+## [1.0.1] - 2025-04-20
+
+### Changed
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+- Remove images and figures
+- Update readme
+
+## [1.0.0] - 2025-04-20
 
 ### Changed
 

README.md

@@ -1,17 +1,17 @@
-# Minimal Goldbach Pairs in Prime Counting
+# 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 Goldbach pair.
+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 $p_j = P$ within the range $6 \leq 2k \leq 2N$.
+We define a function $F_{2N}(P)$ that counts occurrences of $p_i = P$ within the range $6 \leq 2k \leq 2N$.
 
 In particular, the function $F_{2N}(P)$ provides the following identities in terms of prime counting $\pi(2N)$ and
 twin-prime counting $\pi_2(2N)$
 
-$$\pi(2N) = F_{2N}(3) + 1$$
-$$\pi_2(2N) = F_{2N}(3) - F_{2N}(5)$$
+$$\pi(2N) = F_{2N+3}(3) + 1$$
+$$\pi_2(2N) = F_{2N+3}(3) - F_{2N+5}(5)$$
 
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