Mersenne Primes

Tee, Pei Sia (2007) Mersenne Primes. University Malaysia Sabah. (Unpublished)

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Abstract

This dissertation focuses on Mersenne primes, where Mersenne primes are used to generate the corresponding even perfect numbers. Trial-division and Lucas-Lehmer test are used to verify Mersenne primes. The ones digit and tens digit of Mersenne primes are proved by using modular arithmetic. Some patterns of Mersenne numbers are introduced and diagonals of Mersenne's triangle are explored. Even perfect numbers that generated by Mersenne primes are determined by Euclid's theorem and Euler's theorem respectively. The last two digits of even perfect number are proved by using division algorithm and modular arithmetic. Relation of Mersenne primes and even perfect number is studied in triangular number's form.

Item Type: Academic Exercise
Uncontrolled Keywords: Mersenne primes, trial-division, Lucas-Lehmer test, arithmetic, diagonals of Mersenne's triangle
Subjects: Q Science > QA Mathematics
Divisions: SCHOOL > School of Science and Technology
Depositing User: MDM SITI AZIZAH IDRIS
Date Deposited: 19 May 2014 02:21
Last Modified: 13 Oct 2017 03:58
URI: http://eprints.ums.edu.my/id/eprint/9026

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