TY  - JOUR
TI  - Bounded Relative Distances of Symmetric Prime Pairs Around Even Integers
AU  - Ifeyinwa Eunice Daniel
AU  - Olufemi Johnson Ogunsola
PY  - 2026
JO  - African Journal of Mathematics, Statistics and Computer Science
VL  - 1
IS  - 1
SP  - 1-12
DO  - 10.5281/zenodo.20748565
UR  - https://doi.org/10.5281/zenodo.20748565
AB  - This paper investigates the distribution of symmetric prime pairs around the midpoint of even integers. For a given even integer $2n$, prime pairs $(p_1,p_2)$ symmetrically positioned about $n$ are considered, satisfying $$ n-p_1 = p_2-n, $$ or equivalently, $$ p_1+p_2=2n. $$ Particular attention is given to the nearest symmetric prime pair associated with each even integer. Using the symmetric distance $$ d = |n-p_i|,\qquad i=1,2, $$ the relative distance ratio $$ R_n=\frac{d}{n} $$ is introduced as a normalized measure of how far the nearest symmetric prime pair lies from the midpoint. Computational experiments were carried out for selected even integers up to $10^6$. The resulting data exhibit bounded behavior within the tested range and suggest an empirical asymptotic decay of $R_n$ toward zero as $n$ increases, except in cases where the midpoint itself is prime, for which $R_n=0$. Within the computed data, the largest observed ratio occurs at $2n=44$, where $$ R_{22}=\frac{9}{22}=0.4090909\ldots. $$ The paper presents a ratio-based framework for studying local symmetric prime distributions and highlights open questions concerning upper bounds, asymptotic estimates, and the behavior of additional symmetric prime pairs located farther from the midpoint.
ER  -