Sikkema, Djurre Germ (2024) Probable primality testing for Wagstaff primes. Bachelor's Thesis, Mathematics.
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Abstract
This thesis describes multiple probable prime tests specifically designed for Wagstaff numbers. Wagstaff numbers are of the form $W_n = \frac{2^n + 1}{3}$ where $n$ is an odd positive integer. Several properties of Wagstaff numbers are covered and proven. Which allow to describe and prove multiple probable prime tests. A proof of the Lifschitz test is presented and analyzed, which is a derivation of Miller's test. After which a discussion and proof of a generalized probable prime test based on Lucas-Lehmer recurrences is given. Case distinctions of this generalized test are the Anton Vrba test and Robert Gerbicz test. In terms of speed, the Lifschitz test outperforms the Vrba and Gerbicz test. However, these latter two tests provide some insights into finding a prime test that works in both directions. The theory used to prove these tests allows to determine primality for "smaller" Wagstaff numbers in a fairly straightforward manner, which is demonstrated in multiple examples. Finally an argument is given on why an attempted proof on whether there exist infinitely many Wagstaff primes is incorrect.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Top, J. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 08 Aug 2024 13:54 |
| Last Modified: | 08 Aug 2024 13:54 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33908 |
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