The Four-Lane Arrangement of the Primes: a compass layout of primes by last digit — what it shows, what it predicts, and what it does not

Every prime greater than 5 ends in 1, 3, 7 or 9. Placing these four residue classes mod 10 on the points of a compass and letting each class advance independently produces a four-column table in which row n holds the n-th prime of each class. This paper documents the arrangement, verifies its arithmetic, and tests what it can and cannot predict. Three findings are reported. (i) The arrangement makes Chebyshev's bias structurally visible: residue classes 3 and 7 hold the row minimum in 99.9% of rows, and the row ordering persists from one row to the next 97.8% of the time. (ii) The intuitive prediction rule suggested by the layout — that an empty cell indicates the residue of the next prime — is worthless, scoring 25.4% against a 25% baseline, and a hand-checkable counterexample is given. (iii) A different statistic drawn from the same layout — the ordering of the four classes by most recent occurrence — carries measurably more signal than the conventional conditioning on the previous prime's residue, when both are measured against a Cramér-type null model on the mod-10 wheel. A further section measures the direction of the "hand" on the compass and explains its clockwise lean as the prime-gap distribution read through the compass ordering. No new mathematics is claimed. The recency ordering is a deterministic function of the residue history and is therefore subsumed by the Hardy–Littlewood k-tuple framework. The contribution is a compact, visualisable summary statistic and a calibrated measurement of how much it sees. All computations are over primes below 3 × 10^7. The interactive clock, the book and twelve short films are at https://primeticktock.com.