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Primality Testing

Dwarshuis, J.H. (2017) Primality Testing. Bachelor's Thesis, Mathematics.

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Abstract

This thesis deals with the primality of numbers of certain forms. Two methods to develop such tests are described. The first one is the group-order method. This method has been applied to the Mersenne numbers, Mn := 2^n−1, in which case it coincides with the classical Lucas-Lehmer test. The first goal of this thesis is to apply the group-order method to numbers of the form 3·2^n + 1 and 3·2^n −1. This will result in tests that give a condition on when these numbers are prime. However, these tests only work for limited values of n. The second method that is dealt with is the elliptic curve method. Using theory about elliptic curves a test is found for numbers of the form 121·16^n + 1. The tests are implemented in order to generate some large prime numbers.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:29
Last Modified: 15 Feb 2018 08:29
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/15348

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