In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

Introduction: Tuberculosis (TB) is one of the most prevalent respiratory diseases in the world. In 2020 there were at least 9.9 million new infections, with 1.5 million deaths. Approximately 10% of people infected with Mycobacterium tuberculosis (LTBI) develop the disease during the first 2 to 5 years after infection. Currently in South America, the diagnosis of LTBI continues to be per-formed through the Mantoux tuberculin skin test (TST). Objective: The objective of our study was to compare the sensitivity of a new immunofluorescence IGRA test against a widely available IGRA kit on the market. Material and method: Close contact to infectious patients with TB, or HIV patients or immunocompromised for another cause were recruited. Two interferon gamma release assay (IGRA) diagnostic kits were used and compared with TST. Results: 76 patients were recruited. 93.42% were Chilean nationality, 98.68% of the patients did not have immunosuppres-sion. The sensitivity of the new technique was 88.89% and specificity 92.50% in the study popula-tion compared to the IGRA previously used. In the subgroup older than 36 years, the sensitivity was 95.65% and the specificity 89.47%. Conclusion: IGRA techniques are a new resource in clini-cal laboratories to be able to make an accurate diagnosis in LTBI in the region of the Americas. In our population, the greatest benefit of this new IGRA would be observed in people over 36 years of age, where the sensitivity of the technique was like that of the currently available test.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.