Nested 9x9 Unique Emirp Prime Magic Square
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This paper presents an explicit construction of a nested 9×9 magic square composed entirely of distinct emirp primes. An emirp prime is a non-palindromic prime whose decimal reversal is also prime. The construction contains 81 unique emirp primes arranged so that: every row, column, and both principal diagonals sum to the common magic constant115,726,203;each of the nine aligned 3×3 sub-squares is itself magic;the nine centres of those 3×3 sub-squares form a secondary 3×3 magic square;all entries are distinct;every reversed entry is also prime;no palindromic primes occur. The global centre of the square is 12,858,467, and the secondary centre-grid magic constant is 38,575,401. The note is intentionally modest in scope. It does not claim an infinite family theorem, a general construction algorithm for all orders, or that the digit-reversed square itself is magic. Instead, the paper presents a concrete, fully auditable witness showing that emirp primality, recursive 3×3 nesting, uniqueness, and global magic-square structure can coexist simultaneously within a single explicit object. The construction is framed as a short computational note in combinatorics and recreational number theory, with emphasis on reproducibility, verification transparency, and constrained constructive existence rather than asymptotic theory. A companion verification package accompanies the release.



