03 (Old). Gauss’s Estimation – An Epistemological Problem

Chapter 3 of the book: “From Riemann Hypothesis to CPS Geometry and Back  Volume 1 (https://www.amazon.com/dp/B08JG1DLCV) ”, Canadian Intellectual Property Office Registration Number: 1173734 (http://www.ic.gc.ca/app/opic-cipo/cpyrghts/srch.do?lang=eng&page=1&searchCriteriaBean.textField1=1173734&searchCriteriaBean.column1=COP_REG_NUM&submitButton=Search&searchCriteriaBean.andOr1=and&searchCriteriaBean.textField2=&searchCriteriaBean.column2=TITLE&searchCriteriaBean.andOr2=and&searchCriteriaBean.textField3=&searchCriteriaBean.column3=TITLE&searchCriteriaBean.type=&searchCriteriaBean.dateStart=&searchCriteriaBean.dateEnd=&searchCriteriaBean.sortSpec=&searchCriteriaBean.maxDocCount=200&searchCriteriaBean.docsPerPage=10) , Ottawa, ISBN 9798685065292, 2020. On Google Books: https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y On Google Play: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ The text discusses Gauss's attempts to find a pattern in the distribution of prime numbers. The author examines Gauss's early experiments with counting primes and explores his eventual development of a formula to approximate the number of primes less than a given number. The text also highlights the limitations of this formula and the ongoing challenge of finding a precise mathematical expression for the distribution of primes. The author then discusses the Prime Number Theorem, which provides a more accurate approximation for the distribution of primes, and the logarithmic integral as an even better approximation. Finally, the text touches upon the implications of this problem for our understanding of mathematics and the potential need for new approaches to address it.