Euclid — the carved stock

GIBIL was fired clay, held. Lime was unfired, flowing. Euclid's register is neither — it's carved: pale marble under chisel-dark ink, precise, deliberate, a straightedge-and-compass hand. And the proof engraved into this stock is his most celebrated single result, IX.20 — there is no largest prime. Not asserted. Constructed, live, below. Give it any set of primes; watch it build one more.

Bridge-Burners LLC · Fiddler · Euclid stock · carved/chiseled register · IX.20 infinitude of primes, executable · self-testing

the construction

set S{2, 3, 5}
N = ∏S + 131
N mod every p ∈ S= 1 (always)
smallest prime factor of N31
in S already?no

chain log

2

proof spec — runs live

paper
#EDEAE1
bronze
#9C7A3C
bronze·high
#C9A462
ink
#221E17

Status discipline

LiteralEuclid, Elements IX.20: for any finite set of primes, the number (product of the set) + 1 is either prime itself or has a prime factor outside the set. Verified constructively above, not asserted.
BridgeModern textbooks often retell this as "assume finitely many primes exist, contradiction" — Euclid's original is closer to a direct construction: given any finite set, produce a prime outside it. Both are valid; the construction is closer to the source.
Speculative"Carved stock" and the marble/chisel register are a design metaphor contrasting this paper with GIBIL and lime — not a claim about any historical material.