03. Gauss 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 explores the historical development of methods used to estimate the distribution of prime numbers. It begins by highlighting the difficulties faced by mathematicians like Gauss in manually calculating prime numbers, especially for large sets. The text then delves into the idea of using logarithms to approximate the number of primes below a given number, a concept that Gauss himself explored. This leads into a discussion of the Prime Number Theorem, which provides a precise asymptotic formula for the distribution of prime numbers. Finally, the text touches upon the logarithmic integral as a refined approximation for the distribution of primes.