An inquiry into whether or not 1000009 is a prime number
| dc.creator | Euler, Leonhard | |
| dc.date | 2004-12-02 | |
| dc.date | 2008-08-23 | |
| dc.date.accessioned | 2026-07-07T09:57:46Z | |
| dc.date.available | 2026-07-07T09:57:46Z | |
| dc.description | Translation from the Latin original "Utrum hic numerus 1000009 sit primus necne inquiritur" (1778). E699 in the Enestrom index. The idea of this paper is that if some number is a sum of two squares in two ways, then some other smaller number must be a square. We then check all the cases. If we find a case where this smaller number is a square then we can use this to find a factor of the original number, which is therefore composite. If we check all the cases and none of them are squares then the original number can be written as a sum of two squares in only one way, and hence is prime. Euler first examines the number 1000009 and then 1000081. Obviously 1000009=1000^2+3^2, and then he finds that 1000009=972^2+235^2, hence it is not prime. On the other hand, Euler finds that 1000081 can be written as a sum of squares in only one way, hence it is prime. | |
| dc.description | 8 pages; translation rewritten | |
| dc.identifier | https://arxiv.org/abs/math/0412062 | |
| dc.identifier | http://arxiv.org/abs/math/0412062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167468 | |
| dc.subject | History and Overview | |
| dc.subject | Number Theory | |
| dc.subject | 01A50; 11E16; 11Y11 | |
| dc.title | An inquiry into whether or not 1000009 is a prime number | |
| dc.type | text |