AI PROMPT · 70
欧几里得证明动力学排版
创建一个题为“THERE IS NO LAST PRIME”（不存在最后一个素数）的动力学数学证明。 将欧几里得的论证呈现为一个精美的机械检测系统。排版元素转化为刻有数字的轮盘、乘法传送带和余数指示器。 该机制必须演示证明过程，而非仅仅装饰旁白解释。 交付物 一个自包含的 HTML 文件。 1080×1080 分辨率。 20.00 秒循环。 确定性 60fps 渲染。 使用 SVG 和/或 Canvas。 无外部运行时资源。 调色板 瓷白色 #F0EEE6。 石墨色 #222522。 工业绿 #416B53。 警示橙 #E78636。 字体 所有计算使用等宽表格字体。 声明部分使用粗体几何无衬线字体。 最终逻辑陈述使用小型技术衬线字体。 使用严谨的字间距和大号易读的数字。 锁定文案 假设列表结束。 将列表中的每个素数相乘。 加一。 列表中每个素数都留下余数 1。 缺少一个素因子。 不存在最后一个素数。 核心示例 假设列表： 2, 3, 5, 7, 11, 13 乘积： 30030 乘积加一： 30031 因式分解： 30031 = 59 × 509 这两个因子均不在假设列表中。 重要逻辑 不要声称将素数相乘再加一总是产生素数。 构造出的数字可能是合数。 其素因子不能是假设完整列表中的任何素数。 数值示例说明了普遍矛盾。 故事板 0.00–3.00 假设列表结束。 六个刻有素数的轮盘锁定在一个有限的检测架上。 在 13 之后关闭物理限位器。 限位器使“完整性”这一主张变得可见。 3.00–6.50 将列表中的每个素数相乘。 一条传送带耦合所有六个轮盘。 显示可读的乘法表达式： 2 × 3 × 5 × 7 × 11 × 13 = 30030。 仅在运动过程中使用滚动数字；最终值应迅速稳定下来。 6.50–8.50 加一。 一个橙色单位进入机制。 它将输出从 30030 推进到 30031。 使这一单位变化成为决定性的视觉事件。 8.50–12.50 列表中每个素数都留下余数 1。 输出通过六个除法门。 每个门标有其对应的素数。 每个门产生相同的可见余数：1。 排列六个完成的结果，以便观众同时比较它们。 12.50–15.50 输出打开为一个带标签的机械外壳。 内部揭示： 59 × 509。 这些因子无法放入假定的完整架中。 新的因子卡片迫使限位器向外移动。 15.50–18.00 缺少一个素因子。 然后： 不存在最后一个素数。 将一般性陈述保持在打开的架子上方。 包括紧凑的一般形式： N = p₁p₂…pₖ + 1。 N mod pᵢ = 1。 18.00–20.00 重置机制以开始下一个循环。 确保过渡平滑且符合整体美学风格。
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PROMPT
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