History of the Prime Numbers Theorem

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Added on 2021-06-17

History of the Prime Numbers Theorem

Added on 2021-06-17

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1Running head: The History of the Prime Numbers TheoremThe History of the Prime Numbers TheoremInstitutionNameDate

2The History of the Prime Numbers TheoremIntroductionA number is classified as a prime number if it is a whole number and it has only two factors which are 1 and itself. A factor on the other hand is a whole number that can evenly be divided into another number. That is the division quotient should be a whole number. Some examples of prime numbers are 5,13 and 29. The other numbers are classified as composite numbers. Prime numbers have several applications in mathematics which makes them a key part of mathematics. For instance, in the field of Algebra prime numbers are applied to solve proofs. An example being the group theory (Ingemar and Karol, 2017). In addition, the connection of prime numbers with Riemann zeta function makes them applicable during analytical tasks. In this document will review the history of prime numbers theorem and the role of some of the greatest contributors to the theorem.The History of prime numbers theoremThe Prime numbers theorem (PNT) was introduced to illustrate the asymptotic distribution of the prime numbers within the positive integers. The theorem formalizes the insinuation that prime numbers become rare as they increase in size through the quantification of the occurrence rate. All this are summarized by the PNT statement: “For large values of x, π(x) is approximately equal to x/ln(x)”.The first time the PNT was introduced in mathematics was by ancient Greek mathematicians who were trying to study perfect and amicable numbers. In the 200 BC an algorithm for calculating prime numbers known as a sieve of Eratosthenes was designed by the Greek Eratosthenes. From here it took a significant amount of time before important developments were made in this area. This come in the 17th Century when Fermat proved a speculation previously made by Albert Girard that all prime numbers in the form 4n+1can berewritten as a summation of four squares. This technique provided a new way of factoring large numbers (Rudman, 2007).People involved in the development of prime numbers theoremPrime numbers just like other mathematic concept took the effort of several individuals before it could be proven and applied in the current mathematical field. This list involved those who developed the theories, those who proved the theories as well as the mathematicians who managed to gauge the applications of the theories to other mathematical models.

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