素数无穷的文字证明

Create a kinetic mathematical proof titled “THERE IS NO LAST PRIME.”
Stage Euclid’s argument as a beautiful mechanical inspection system. Typography becomes engraved number wheels, multiplication belts, and remainder indicators.
The mechanism must demonstrate the proof rather than decorate a narrated explanation.
DELIVERABLE
One self-contained HTML file.
1080×1080.
20.00-second loop.
Deterministic 60fps rendering.
Use SVG and/or Canvas.
No external runtime assets.
PALETTE
Porcelain # F0EEE6.
Graphite #222522.
Industrial green # 416B53.
Warning orange # E78636.
TYPE
Tabular monospace for all calculations.
Heavy geometric grotesque for declarations.
Small technical serif for the final logical statement.
Use disciplined spacing and large, readable numerals.
LOCKED COPY
SUPPOSE THE LIST ENDS.
MULTIPLY EVERY PRIME ON IT.
ADD ONE.
EVERY LISTED PRIME LEAVES REMAINDER 1.
A PRIME FACTOR IS MISSING.
THERE IS NO LAST PRIME.
CENTRAL EXAMPLE
Assumed list:
2, 3, 5, 7, 11, 13
Product:
30030
Product plus one:
30031
Factorization:
30031 = 59 × 509
Both factors are absent from the assumed list.
IMPORTANT LOGIC
Do not claim that multiplying primes and adding one always produces a prime.
The constructed number may be composite.
Its prime factors cannot be any prime on the assumed complete list.
The numerical example illustrates the general contradiction.
STORYBOARD
0.00–3.00
SUPPOSE THE LIST ENDS.
Six engraved prime wheels lock into a finite inspection rack.
A physical end-stop closes after 13.
The end-stop makes the claim of completeness visible.
3.00–6.50
MULTIPLY EVERY PRIME ON IT.
A belt couples all six wheels.
Show a readable multiplication expression:
2 × 3 × 5 × 7 × 11 × 13 = 30030.
Use rolling numerals only during movement; settle the final value sharply.
6.50–8.50
ADD ONE.
A single orange unit enters the mechanism.
It advances the output from 30030 to 30031.
Make this one-unit change the decisive visual event.
8.50–12.50
EVERY LISTED PRIME LEAVES REMAINDER 1.
The output passes through six division gates.
Each gate is labelled with its prime.
Each produces the same visible remainder: 1.
Arrange the six completed results so the audience can compare them simultaneously.
12.50–15.50
The output opens as a labelled mechanical casing.
Inside, reveal:
59 × 509.
These factors cannot fit into the supposedly complete rack.
The end-stop is forced outward by the new factor cards.
15.50–18.00
A PRIME FACTOR IS MISSING.
Then:
THERE IS NO LAST PRIME.
Hold the general statement above the opened rack.
Include the compact general form:
N = p₁p₂…pₖ + 1.
N mod pᵢ = 1.
18.00–20.00
A fresh inspection plate slides over the mechanism.
Its engraved edge becomes the original end-stop.
Reset the hidden wheels.
Reveal the opening rack at the exact initial position.
REQUIRED MOTION
Every mechanical action must correspond to an operation in the proof.
Use linked rota