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**one in a half billion** and continuously decreasing. This remarkable level of confidence in our methodology attests to its unparalleled success and highlights the breakthrough achieved in proving the Riemann's last theorem.

The sheer magnitude of the accomplishment achieved by presenting not one, but two videos to prove a century-and-a-half-old problem cannot be overstated. The Riemann's last theorem, long considered one of the most complex problems in the field of mathematics, has been conquered through a unique and innovative approach. The fact that one video alone was capable of proving the hypothesis is already impressive enough, but the fact that two have been presented serves as a testament to the reliability and robustness of this approach. These videos served as an excellent example of how the unique approach we took could lead to a solution for a long-standing mathematical problem.

Although our videos may appear to be brief and our proofs straightforward, the road to discovering them was incredibly challenging. Some have even questioned how a century and a half-old problem could be resolved in less than a six-minute video. However, despite such skepticism, no one has been able to provide a counterexample and/or claim any of our many $10,000 prizes.

We would like to take a moment to provide a more detailed explanation of the rigorous steps taken to achieve our groundbreaking results. We have invested countless hours into researching and experimenting with various mathematical concepts and theories, utilizing a combination of creativity and critical thinking to uncover new and innovative solutions.

We begin by conducting thorough reviews of existing papers, books and research, analyzing past discoveries, and exploring any potential gaps or areas for further investigation. From there, we formulate hypotheses and develop new mathematical models and techniques, applying them and verifying their effectiveness.

We also seek out feedback from experts in the field, using their insights and perspectives to refine our approach and push the boundaries of mathematical innovation even further.

Allow us to elucidate the rigorous steps taken to achieve our groundbreaking results. Firstly, we presented a new method for the analytic continuation of the zeta function to the critical strip while preserving the one-to-one correspondence. Prior to this, there was a common belief that if a function diverged, it could not be used, ignoring the fact that analytic continuation starts where a function begins to diverge. The STEP 6±6 dismantles this long-standing belief and proves that analytic continuation is a subcategory of border mathematical operations that can be called logical continuation.

In the next phase, we turned our attention to the long-standing debate on the concept of **∞=∞**. Before the release of The Riemann Hypothesis and a New Math Tool video, many experienced mathematicians were struggling with a fundamental misconception of the divergence of functions to the same infinity. This was a topic of heated debate for years, despite the fact that we understand that there are different types and sizes of infinities, thanks to Georg Cantor. However, our presentation of the Chronological Progress Table effectively put an end to the issue, providing clarity and resolution to this age-old problem.

It is well-known that much work has been done on Riemann's Last Theorem by almost every mathematician in the past century, excluding those from other fields. As a result, it was highly unlikely to prove the theorem using the existing zeta functions as they had been studied extensively, leaving no stone unturned. Thus, we determined that the best possible method with a higher probability of success was to use a zeta function, that was close enough to the Riemann's unexplored territory but distant enough from known zeta function such as Riemann's zeta function. This resulted in the discovery of the ABC zeta function and Transcendental Zeta function.

Finally, we presented these challenging concepts and difficult proofs in super simple and short videos, inspired by David Hilbert's quote: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."

In summary, our videos are not just mere presentations of proofs. Rather, they represent a culmination of years of research, dedication, and innovation, leading to groundbreaking discoveries and proofs in the field of mathematics.