Aydın Tiryaki (2026)

This major experiment, designed to measure the boundaries of artificial intelligence models, is the fruit of a journey that began with a single simple question and deepened step by step. This article documents how an AI (Gemini) was matured through user guidance and how the “Master Prompt,” which will test other AIs, was ultimately produced through reverse engineering from this refined knowledge.

Process Development: Incremental Architecture

Our experiment consisted of four main stages that rose from the bottom up, rather than a “top-down” command:

1. Data Discovery: The process began with the identification of Fibonacci primes up to 1,000.
2. In-depth Analysis: After the basic list was established, the relationship between primality and the index (position number), divisibility rules, and exceptions like n=4 that break the system were examined one by one.
3. The Gold Standard Article: All this data was compiled by Gemini to create the core article titled “The Dance of Numbers,” which serves as the project’s reference point.
4. Reverse Engineering: Once the information reached its peak level, a comprehensive prompt (command set) was designed by working backward from the existing article to see if other AI models could capture this depth from scratch.

Strategic Goal

Our goal here is this: Can other models like ChatGPT, Claude, and DeepSeek (or even Gemini itself) replicate this high-quality result—attained with Gemini through step-by-step guidance—using only a single command and performing their own internal research? This “Discovery Prompt” is a performance scale that measures the true reasoning capacity of these models.

The Core of the Experiment: The Master Prompt

The following text is the standardized command set that will be given to all AI models involved in the experiment under identical conditions. Even a single character change in this text would compromise the “fair comparison” (benchmarking) nature of the experiment.

Introduction and Request: You are an artificial intelligence with the characteristics of an expert science writer and mathematician with a global knowledge base. Could you prepare a comprehensive article in entirely Turkish that explores the relationship between the Fibonacci sequence and Prime numbers by fulfilling the following research tasks?

Research and Writing Tasks:

1. Historical Background: I request that you research and explain the origins of the Fibonacci sequence and the mathematician who introduced this sequence to Europe, along with the relevant work.
2. Character Analysis: Could you explain, using scientific terms, the fundamental difference between the growth rates of the Fibonacci sequence and Prime numbers by comparing their progression along the number line?
3. Statistical Comparison: By examining the limits of 1,000, 1,000,000, and 1,000,000,000 (one billion), could you identify and present in a table how many prime numbers, how many Fibonacci numbers, and how many “Fibonacci primes” are within each limit?
4. Solving the Relationship: Could you analyze and explain the mathematical relationship between a Fibonacci number being prime and its position (index) in the sequence?
5. Finding Anomalies: Could you research and detail all exceptions and deviation points (cases where the character of the index and the character of the result do not match) that break the general rule you found above?
6. Rarity Evaluation: Based on the statistics you have obtained, could you perform a concluding analysis on why the intersection points of these two sets of numbers are so rare?

Technical Rules:

• Language: I request that the article be written in fluent Turkish with academic rigor.
• Format: The text should be scannable, using subheadings, tables, and bullet points.
• LaTeX Prohibition: Do not use LaTeX format for any mathematical expressions; please write all formulas and numbers as plain text suitable for copying.

Mandatory Closing Section: At the very end of the article, could you add the following information in a single paragraph?

• The name/version of the AI model that prepared this article.
• The exact date (dd.mm.yyyy) and time (hh:mm) the process was completed.
• A short note about the working mode or performance level.

Results and Expectations

This study is an example of how AI can be guided not just as a knowledge repository, but as a working partner. In the later stages of our series, we will see the limits of digital intelligence together by comparing the outputs of this “reverse-engineered” prompt across different models based on accuracy, depth, and consistency.

| aydintiryaki.org | YouTube | Aydın Tiryaki’nin Yazıları ve Videoları │Articles and Videos by Aydın Tiryaki | Bilgi Merkezi│Knowledge Hub  | ░ “Yapay Zeka” ve “Fibonacci ve Asalların Kesiştiği Nadir Dünya” │ AI and “The Rare World Where Fibonacci and Primes Intersect” ░ 12.02.2026

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A Note on Methods and Tools: All observations, ideas, and solution proposals in this study are the author’s own. AI was utilized as an information source for researching and compiling relevant topics strictly based on the author’s inquiries, requests, and directions; additionally, it provided writing assistance during the drafting process. (The research-based compilation and English writing process of this text were supported by AI as a specialized assistant.)