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
中文译文
创作一场标题为“THERE IS NO LAST PRIME.”的动态数学证明。
把欧几里得的论证布置成一套精美的机械检验系统。字体化为刻蚀的数字轮、乘法传动带和余数指示器。
机械结构必须演示这一证明，而不是为旁白解释做装饰。
交付物
一个自包含的 HTML 文件。
1080×1080。
20.00 秒循环。
确定性的 60fps 渲染。
使用 SVG 和/或 Canvas。
不使用任何外部运行时资源。
配色
瓷白 # F0EEE6。
石墨 #222522。
工业绿 # 416B53。
警示橙 # E78636。
字体
所有计算使用等宽字体与表格数字。
宣言使用厚重的几何无衬线体。
最终逻辑陈述使用小型技术感衬线体。
使用严谨的间距和硕大、清晰可读的数字。
锁定文案
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
假设的列表：
2, 3, 5, 7, 11, 13
乘积：
30030
乘积加一：
30031
因式分解：
30031 = 59 × 509
这两个因子都不在假设的列表中。
重要逻辑
不要声称把质数相乘再加一总能得到质数。
构造出的数可能是合数。
它的质因数不可能是假设中那份完整列表上的任何质数。
这个数值示例说明的是一般性的矛盾。
分镜
0.00–3.00
SUPPOSE THE LIST ENDS.
六个刻蚀的质数轮锁定进一个有限的检验架。
一个实体止挡在 13 之后闭合。
这个止挡让“完整”的断言变得可见。
3.00–6.50
MULTIPLY EVERY PRIME ON IT.
一条传动带连接全部六个轮子。
显示一个清晰可读的乘法表达式：
2 × 3 × 5 × 7 × 11 × 13 = 30030.
仅在运动过程中使用滚动数字；最终数值要干脆地落定。
6.50–8.50
ADD ONE.
一个橙色单位进入机械结构。
它把输出从 30030 推进到 30031。
让这一单位的改变成为决定性的视觉事件。
8.50–12.50
EVERY LISTED PRIME LEAVES REMAINDER 1.
输出经过六道除法闸门。
每道闸门都标注其对应的质数。
每一道都产生同样可见的余数：1。
把这六个完成的结果排布好，让观众可以同时比较。
12.50–15.50
输出打开，成为一个带标签的机械外壳。
内部露出：
59 × 509.
这些因子无法装进这个号称完整的架子。
新的因子卡片把止挡向外顶开。
15.50–18.00
A PRIME FACTOR IS MISSING.
接着：
THERE IS NO LAST PRIME.
把一般性陈述保持在打开的架子上方。
加入紧凑的一般形式：
N = p₁p₂…pₖ + 1.
N mod pᵢ = 1.
18.00–20.00
一块新的检验板滑到机械结构上方。
它刻蚀的边缘成为最初的止挡。
重置隐藏的轮子。
在精确的初始位置重新露出开场时的检验架。
必需的运动
每一个机械动作都必须对应证明中的一步操作。
使用联动的旋转
