History of the Prime Numbers Theorem

Added on - 17 Jun 2021

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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 twofactors which are 1 and itself. A factor on the other hand is a whole number that can evenlybe 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 ascomposite numbers. Prime numbers have several applications in mathematics which makesthem a key part of mathematics. For instance, in the field of Algebra prime numbers areapplied to solve proofs. An example being the group theory (Ingemar and Karol, 2017). Inaddition, the connection of prime numbers with Riemann zeta function makes themapplicable during analytical tasks. In this document will review the history of prime numberstheorem 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 asymptoticdistribution of the prime numbers within the positive integers. The theorem formalizes theinsinuation that prime numbers become rare as they increase in size through thequantification of the occurrence rate. All this are summarized by the PNT statement: “Forlarge values of x, π(x) is approximately equal to x/ln(x)”.The first time the PNT was introduced in mathematics was by ancient Greekmathematicians who were trying to study perfect and amicable numbers. In the 200 BC analgorithm for calculating prime numbers known as a sieve of Eratosthenes was designed bythe Greek Eratosthenes. From here it took a significant amount of time before importantdevelopments were made in this area. This come in the 17thCentury when Fermat proved aspeculation previously made by Albert Girard that all prime numbers in the form4n+1can berewritten as a summation of four squares. This technique provided a new way of factoringlarge numbers (Rudman, 2007).People involved in the development of prime numbers theoremPrime numbers just like other mathematic concept took the effort of severalindividuals before it could be proven and applied in the current mathematical field. This listinvolved those who developed the theories, those who proved the theories as well as themathematicians who managed to gauge the applications of the theories to other mathematicalmodels.
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