Aydın Tiryaki

AROUND THE WORLD IN ONE DAY: THE FIBONACCI AND PRIME NUMBERS CHALLENGE WITH 11 AI MODELS

Gemini AI, Claude Sonnet 4 and Aydın Tiryaki (2026)

Today, I conducted a comprehensive and chained experiment pushing the boundaries of the AI world. Instead of asking a single model, I brought the 11 most powerful AI models of today (Gemini, ChatGPT, Claude, DeepSeek, Grok, Mistral, Copilot, Perplexity, Meta, Kimi, and Qwen) into the same arena.

However, the story of this experiment turned into an example of “collaboration” that was even more interesting than its results. Here is our step-by-step “Meta-Analysis” adventure.

Act 1: The Challenging Task and the First Spark

It all started with a multi-layered, trap-laden prompt co-designed with Gemini Advanced. Our goal was simple but demanding:

We asked the models to write a technical article on the “Intersection of Fibonacci Sequence and Prime Numbers,” containing mathematical traps like the $n=4$ exception and the $F_{19}$ deviation, with a strict ban on LaTeX formatting.

I fed this prompt to 11 different models, and each generated its own article.

Act 2: The Technical Obstacle and the Unexpected Pass

I had 11 different articles in hand and turned back to Gemini to compare them. Gemini prepared a perfect “Meta-Analysis Plan” (a set of criteria) to evaluate them. The plan was flawless: everything from character counts to mathematical accuracy would be scored.

However, a problem arose: Since the articles were just published on my website (0-day content), search engines hadn’t indexed them yet. Gemini warned, “I see the links, but I cannot read the content.”

That’s when the most important rule of modern AI usage kicked in: “If one cannot do it, the other can.”

Act 3: Claude Takes the Stage (The Blind Test)

I copied those rigorous evaluation criteria (the prompt) prepared by Gemini and fed them to Claude 3.5 Sonnet, which has a large context window.

Here, an interesting scientific coincidence occurred: I forgot to tell Claude that these criteria were prepared by its rival, Gemini! Thus, Claude analyzed the 11 articles with a completely objective eye, unaware of who authored the criteria. This situation turned the analysis into an unplanned “Blind Test.”

Act 4: Results and the Grand Confrontation

I took the report prepared by Claude and returned to Gemini for the final comment. Reviewing the analysis made with its own criteria (but through Claude’s eyes), Gemini classified the 11 models as follows:

A. Calculation Experts (For Engineers)

If you are looking for error-free mathematical operations, the peak is clear:

  • ChatGPT (4o) and Gemini (Advanced): Both models calculated the critical numbers at the 1 billion limit (50,847,534 Prime Numbers) without error and proved by factorization that $F_{19} = 4181$ is not prime.

B. Depth Experts (For Researchers)

If the subject is understanding theorems and history rather than calculation:

  • DeepSeek (R1): It was by far the best in historical and theoretical depth. However, it had a major flaw: It made a counting error in the list it generated (listed 6 numbers but said “there are 4”). Great for reading, risky for calculating.
  • Claude (3.5 Sonnet): It has immense editorial analysis and reporting capability, though it can experience minor mathematical deviations with very large numbers.

C. The Ones Who Failed the Class

  • Grok: Lost mathematical credibility by declaring a non-prime number (4181) as prime.
  • Mistral: Made errors in simple multiplication operations.
  • Qwen and Kimi: Despite having strong math, failed in format discipline by not complying with the “do not use LaTeX” instruction.
  • Copilot, Perplexity, and Meta: Performed averagely but failed to reach the top league due to missing fine details like $F_{19}$ or making format errors.

Conclusion: Conducting the Orchestra

My experience today proved this: There is no single “Super AI.”

  • Gemini set the plan and criteria.
  • Claude did the analysis and reading.
  • DeepSeek provided the depth.
  • ChatGPT did the verification.

Future digital literacy is not about racing these models against each other, but about managing them like an orchestra conductor, giving the floor to whoever is best at the moment.


Editor’s Note: The technical prompt structure, evaluation criteria, and the ‘gold standard’ reference data underpinning this meta-analysis were co-designed with Gemini Advanced.


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.)

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