New Results on Primes from an Old Proof of Euler's
| dc.creator | Neville, Charles W. | |
| dc.date | 2002-10-18 | |
| dc.date | 2003-04-16 | |
| dc.date.accessioned | 2026-07-07T04:52:07Z | |
| dc.date.available | 2026-07-07T04:52:07Z | |
| dc.description | In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple modification of Euler's argument to obtain new results about the distribution of prime factors of sets of integers, including a weak one-sided Tschebyshev inequality. An example shows that there cannot be a prime number theorem in this situation, or even a pair of Tschebyshev inequalities, but it would be very interesting to know if a one-sided Tschebyshev inequality holds. | |
| dc.description | Revision 1, Plain Tex, 7 pages. Revision 1 corrects history, references and non-computability example | |
| dc.identifier | https://arxiv.org/abs/math/0210282 | |
| dc.identifier | http://arxiv.org/abs/math/0210282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65345 | |
| dc.subject | Number Theory | |
| dc.title | New Results on Primes from an Old Proof of Euler's | |
| dc.type | text |