PRIMEGAPS
Gaps between primes and almost primes. Patterns in primes and almost primes. Approximations to the twin prime and Goldbach conjectures
| Coordinatore | MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Hungary [HU] |
| Totale costo | 1˙376˙400 € |
| EC contributo | 1˙376˙400 € |
| Programma | FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | ERC-2008-AdG |
| Funding Scheme | ERC-AG |
| Anno di inizio | 2008 |
| Periodo (anno-mese-giorno) | 2008-11-01 - 2013-10-31 |
Partecipanti
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|---|---|---|---|---|
| 1 |
MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Organization address
address: REALTANODA STREET 13-15 contact info |
HU (Budapest) | hostInstitution | 0.00 |
| 2 |
MAGYAR TUDOMANYOS AKADEMIA RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Organization address
address: REALTANODA STREET 13-15 contact info |
HU (Budapest) | hostInstitution | 0.00 |
Mappa
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Obiettivo del progetto (Objective)
'The twin prime conjecture, that n and n2 are infinitely often primes simultaneously, is probably the oldest unsolved problem in mathematics. De Polignac (1849) conjectured that for every even value of h, n and nh are infinitely often primes simultaneously. These are the most basic problems on gaps and patterns in primes. Another one is the conjecture of Waring (1770), stating that there are arbitrarily long arithmetic progressions (AP) of primes. For the newest developments we cite Granville (Bull. AMS 43 (2006), p.93): ): Despite much research of excellent quality, there have been few breakthroughs on the most natural questions about the distribution of prime numbers in the last few decades. That situation has recently changed dramatically with two extraordinary breakthroughs, each on questions that the experts had held out little hope for in the foreseeable future. Green and Tao proved that there are infinitely many k-term arithmetic progressions of primes using methods that are mostly far removed from mainstream analytic number theory. Indeed, their work centers around a brilliant development of recent results in ergodic theory and harmonic analysis. Their proof is finished, in a natural way, by an adaptation of the proof of the other fantastic new result in this area, Goldston, Pintz and Yildirim s proof that there are small gaps between primes. The proposal's aim is to study these types of patterns in primes with possible combination of the two theories. We quote 3 of the main problems, the first one being the most important. 1) Bounded Gap Conjecture. Are there infinitely many bounded gaps between primes? 2) Suppose that primes have a level of distribution larger than 1/2. Does a fixed h exists such that for every k there is a k-term AP of generalised twin prime pairs (p, ph)? 3) Erdôs' conjecture for k=3. Suppose A is a sequence of natural numbers, such that the sum of their reciprocals is unbounded. Does A contain infinitely many 3-term AP's?'