Constructing and Certifying Large Equal-Sum Digit-Reversible Magic Squares of Distinct Emirp Primes

This publication presents a computational and mathematical framework for constructing large magic squares composed of distinct strict emirp primes, where reversing the decimal digits of every entry produces another magic square with exactly the same numerical magic constant. The research documents four constructions of orders **243×243, 729×729, 2,187×2,187 and 6,561×6,561**. The largest contains **43,046,721 distinct eleven-digit strict emirp primes**, with a common forward and reversed magic constant of **360,392,123,027,393**. The paper develops a construction methodology based on complementary prime pairs, balanced triples, exact additive corrections, digit-reversal congruences and controlled within-row permutations. It introduces a deterministic reference algorithm for correcting column and diagonal sums, alongside mathematical results concerning correction reachability and conditional completion. A further theoretical contribution establishes an obstruction to fully recursively aligned ternary magic squares composed entirely of strict emirps when equal forward and reversed global magic constants are required. The work distinguishes mathematical proofs, recorded computational verification, observed construction behaviour and unresolved questions. It discusses construction failure modes, candidate-prime capacity, computational certification and reproducibility. The accompanying research documentation describes verification methods, construction certificates and requirements for independent reproduction. The reported large-scale results are based on project verification records; independent external reproduction and complete public deposition of the numerical evidence remain outstanding. **Author:** Roberto Carlo Angelone **Affiliation:** Independent Researcher, Malta **Research areas:** Number Theory, Computational Mathematics, Recreational Mathematics, Prime Numbers, Magic Squares **Keywords:** Emirp Primes, Reversible Primes, Magic Squares, Digit Reversal, Equal-Sum Magic Squares, Computational Number Theory, Mathematical Constructions, Exact Verification, Reproducible Research.