Reproducible MATLAB Visualisation and Residual Mapping of Base-10 Palindromic Primes below One Hundred Million across Residues Modulo Nine and Modulo Eleven

Palindromic primes are subject to digit symmetry constraints; for example, every even-digit palindrome in base ten is divisible by eleven, so eleven is the only even-digit palindromic prime. The congruence that an integer is equal modulo nine to the sum of its decimal digits makes residues modulo nine a natural focus for digit-sum-based analysis. To provide a fully reproducible empirical picture of these arithmetic constraints, the author of this study implemented a single-file MATLAB workflow that enumerates palindromic integers by mirroring left halves, applies vectorised primality testing, computes digit sums and residues modulo 9 and 11, and aggregates counts into a digit-by-residue counts cube. The pipeline writes canonical CSV and MAT artefacts, exports publication-quality graphics, and reports contingency-table diagnostics including Pearson chi-square testing, standardised residual mapping, Cramer’s V effect size, and Benjamini–Hochberg false discovery rate (FDR) control across the nine-by-eleven joint residue family. The canonical output lists 781 palindromic primes below one hundred million and is strongly concentrated at odd digit lengths, with a median of seven and 668 seven-digit primes. Visual inspection and residual mapping reveal modest local deviations in joint residue cells, with raw counts of up to 16, a maximum standardised residual of about 2.80 and the smallest unadjusted two-sided residual p-value of about 0.0050; the corresponding minimum Benjamini–Hochberg q-value is about 0.499, yielding no discoveries at FDR 0.05. The aggregated nine-by-eleven table is consistent with independence (chi-square (80) = 90.48, p = 0.198) with a small-to-moderate association magnitude (Cramer’s V = 0.120). Per-digit decomposition variables are produced to support stratified inspection of residue patterns, and the numerically dominant seven-digit stratum largely governs the aggregated structure. All implementation choices are consistent with safe numeric practice for this bound; for example, the use of double precision for primality tests is safe for integers well below 2^53, and the code and data artefacts permit exact reproduction.