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
中文翻譯
創作一場標題爲“THERE IS NO LAST PRIME.”的動態數學證明。
把歐幾裏得的論證佈置成一套精美的機械檢驗系統。字體化爲刻蝕的數字輪、乘法傳動帶和餘數指示器。
機械結構必須演示這一證明，而不是爲旁白解釋做裝飾。
交付物
一個自包含的 HTML 文件。
1080×1080。
20.00 秒循環。
確定性的 60fps 渲染。
使用 SVG 和/或 Canvas。
不使用任何外部運行時資源。
配色
瓷白 # F0EEE6。
石墨 #222522。
工業綠 # 416B53。
警示橙 # E78636。
字體
所有計算使用等寬字體與表格數字。
宣言使用厚重的幾何無襯線體。
最終邏輯陳述使用小型技術感襯線體。
使用嚴謹的間距和碩大、清晰可讀的數字。
鎖定文案
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.
核心示例
假設的列表：
2, 3, 5, 7, 11, 13
乘積：
30030
乘積加一：
30031
因式分解：
30031 = 59 × 509
這兩個因子都不在假設的列表中。
重要邏輯
不要聲稱把質數相乘再加一總能得到質數。
構造出的數可能是合數。
它的質因數不可能是假設中那份完整列表上的任何質數。
這個數值示例說明的是一般性的矛盾。
分鏡
0.00–3.00
SUPPOSE THE LIST ENDS.
六個刻蝕的質數輪鎖定進一個有限的檢驗架。
一個實體止擋在 13 之後閉合。
這個止擋讓“完整”的斷言變得可見。
3.00–6.50
MULTIPLY EVERY PRIME ON IT.
一條傳動帶連接全部六個輪子。
顯示一個清晰可讀的乘法表達式：
2 × 3 × 5 × 7 × 11 × 13 = 30030.
僅在運動過程中使用滾動數字；最終數值要乾脆地落定。
6.50–8.50
ADD ONE.
一個橙色單位進入機械結構。
它把輸出從 30030 推進到 30031。
讓這一單位的改變成爲決定性的視覺事件。
8.50–12.50
EVERY LISTED PRIME LEAVES REMAINDER 1.
輸出經過六道除法閘門。
每道閘門都標註其對應的質數。
每一道都產生同樣可見的餘數：1。
把這六個完成的結果排布好，讓觀衆可以同時比較。
12.50–15.50
輸出打開，成爲一個帶標籤的機械外殼。
內部露出：
59 × 509.
這些因子無法裝進這個號稱完整的架子。
新的因子卡片把止擋向外頂開。
15.50–18.00
A PRIME FACTOR IS MISSING.
接着：
THERE IS NO LAST PRIME.
把一般性陳述保持在打開的架子上方。
加入緊湊的一般形式：
N = p₁p₂…pₖ + 1.
N mod pᵢ = 1.
18.00–20.00
一塊新的檢驗板滑到機械結構上方。
它刻蝕的邊緣成爲最初的止擋。
重置隱藏的輪子。
在精確的初始位置重新露出開場時的檢驗架。
必需的運動
每一個機械動作都必須對應證明中的一步操作。
使用聯動的旋轉
