Infinite primes (Shakespeare)
creative proof prompt example
TL;DR（中文）
- 这是一个 “数学证明 + 风格写作” 的
creativity测试：在保持 proof 核心逻辑的同时，用 Shakespeare dialogue 的形式表达。 - 适合用于：风格迁移、长文本结构控制、以及在强约束下生成连贯内容。
- 关键风险：风格到位但 proof 逻辑错；建议要求输出中显式包含关键步骤（例如 Euclid-style construction），并用
evaluation检查逻辑完整性。
Background
The following prompt tests an LLM's capabilities to write a proof that there are infinitely many primes in the style of a Shakespeare play.
How to Apply（中文）
把这个 prompt 用在类似任务时，可以把约束拆成两层：
- Content constraints：必须包含哪些核心论证步骤（proof skeleton）
- Style constraints：用什么 voice、结构、修辞（dialogue, stage directions）
例如对数学 proof，可以先要求模型输出一个简短的 proof outline（英文术语保留），再让它把 outline 改写成特定风格。
How to Iterate（中文）
- 强制包含关键 proof step（例如 “construct N = p1p2...*pk + 1”）
- 增加结构：每个角色负责一个步骤（setup → contradiction → conclusion）
- 加
self-check：最后用 3-5 行总结 proof 的逻辑链（避免风格掩盖错误） - 控制长度：指定 acts/scenes 或 token budget
Self-check rubric（中文）
- proof 是否完整且无明显逻辑漏洞？
- dialogue 是否保持 Shakespeare style（一致的 voice）？
- 是否能把数学步骤表达清楚（读者可复核）？
- 是否避免引入不相关的分支与跑题？
Practice（中文）
练习：把同一个 proof skeleton 分别改写成 3 种风格：
- Shakespeare dialogue
- courtroom cross-examination
- a children’s story
然后用同一个 rubric 检查 proof 是否仍然成立。
Prompt
Write a proof of the fact that there are infinitely many primes; do it in the style of a Shakespeare play through a dialogue between two parties arguing over the proof.
Code / API
OpenAI (Python)
from openai import OpenAI
client = OpenAI()
response = client.chat.completions.create(
model="gpt-4",
messages=[
{
"role": "user",
"content": "Write a proof of the fact that there are infinitely many primes; do it in the style of a Shakespeare play through a dialogue between two parties arguing over the proof.",
}
],
temperature=1,
max_tokens=1000,
top_p=1,
frequency_penalty=0,
presence_penalty=0,
)
Fireworks (Python)
import fireworks.client
fireworks.client.api_key = "<FIREWORKS_API_KEY>"
completion = fireworks.client.ChatCompletion.create(
model="accounts/fireworks/models/mixtral-8x7b-instruct",
messages=[
{
"role": "user",
"content": "Write a proof of the fact that there are infinitely many primes; do it in the style of a Shakespeare play through a dialogue between two parties arguing over the proof.",
}
],
stop=["<|im_start|>", "<|im_end|>", "<|endoftext|>"],
stream=True,
n=1,
top_p=1,
top_k=40,
presence_penalty=0,
frequency_penalty=0,
prompt_truncate_len=1024,
context_length_exceeded_behavior="truncate",
temperature=0.9,
max_tokens=4000,
)