Consecutive Prime Magic Squares

This record contains a family of large consecutive-prime magic squares together with verification tooling, audit summaries, checksum manifests, and companion documentation. The constructions currently include orders: - 81×81- 243×243- 729×729- 2187×2187 together with a larger 6561×6561 candidate currently undergoing final deterministic audit verification. Each verified construction satisfies the following conditions: - all entries are prime;- all entries are distinct;- the entries form a contiguous interval of consecutive primes;- every row sums to the same magic constant;- every column sums to the same magic constant;- both principal diagonals sum to the same magic constant. The project is constructive and computational in nature. No claim is made regarding infinite-family existence, optimality, recursive nesting, or general prime-distribution theorems. The release includes: - dataset files;- SHA-256 checksum manifests;- deterministic verification tooling;- smoke-test audit summaries;- JSON/TXT verification reporting;- GUI and command-line verifier modes;- laptop-safe large-scale verification workflows;- and companion paper documentation. The verifier package supports:- shape verification;- primality verification;- uniqueness verification;- consecutive-prime interval verification;- row/column/diagonal verification;- checksum integrity auditing;- and optional aligned nested-block diagnostics. For ultra-large objects such as the 6561×6561 candidate, the verifier includes streaming, bucketed disk-backed verification modes designed for consumer hardware environments. This consecutive-prime family is mathematically distinct from the author’s earlier recursive nested unique-prime magic-square constructions. No recursive nesting claim is made for the present datasets unless separately stated. Current status classification: - 81×81: computationally verified- 243×243: computationally verified- 729×729: computationally verified- 2187×2187: deterministic audit completed- 6561×6561: constructed candidate under final deterministic verification The purpose of this release is to provide explicit, auditable computational objects together with the infrastructure required for independent verification and reproducibility.