Proth Numbers
In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.
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| Format: | Article |
| Language: | English |
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Sciendo
2014-06-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2014-0013 |
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doaj-54c23c077d6d4846b8a80f4fb26807a9 |
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Article |
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doaj-54c23c077d6d4846b8a80f4fb26807a92021-09-05T21:01:03ZengSciendoFormalized Mathematics1898-99342014-06-0122211111810.2478/forma-2014-0013forma-2014-0013Proth NumbersSchwarzweller Christoph0WSB Schools of Banking Gdańsk, PolandIn this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.https://doi.org/10.2478/forma-2014-0013prime numberspocklington’s theoremproth’s theorempepin’s theorem11a4103b35 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Schwarzweller Christoph |
| spellingShingle |
Schwarzweller Christoph Proth Numbers Formalized Mathematics prime numbers pocklington’s theorem proth’s theorem pepin’s theorem 11a41 03b35 |
| author_facet |
Schwarzweller Christoph |
| author_sort |
Schwarzweller Christoph |
| title |
Proth Numbers |
| title_short |
Proth Numbers |
| title_full |
Proth Numbers |
| title_fullStr |
Proth Numbers |
| title_full_unstemmed |
Proth Numbers |
| title_sort |
proth numbers |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1898-9934 |
| publishDate |
2014-06-01 |
| description |
In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime. |
| topic |
prime numbers pocklington’s theorem proth’s theorem pepin’s theorem 11a41 03b35 |
| url |
https://doi.org/10.2478/forma-2014-0013 |
| work_keys_str_mv |
AT schwarzwellerchristoph prothnumbers |
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1717781704820654080 |