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Primality Testing

Sluis, P.A. van der (2016) Primality Testing. Bachelor's Thesis, Mathematics.

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Abstract

This thesis discusses the primality of two types of numbers. In 1857, French mathematician Édouard Lucas stated that 2^{127}-1 was a prime number. In the 1930s, American mathematician Derrick Lehmer came up with a simple test for finding primes of the form 2^n-1. In this thesis I give a detailed proof of a more general version of this test, based on the unpublished notes from Jaap Top. After that, a part of the proof will be modified to make variations and find different prime tests. The second type of numbers are of the form Kn:=3^{2^n}-3^{2^{n-1}}+1. I will give an necessary and sufficient condition for primes of this form, but only proof the necessary part of it. This proof is based on elliptic curves. The last part of this thesis is used to discuss several important differences between the two tests.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:11
Last Modified: 15 Feb 2018 08:11
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/13827

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