# Landau's Problems on Primes

ARGOMENTI: Convegni Dottorato

SEMINARIO DOTTORATO
Mercoledi prossimo 30/05, il Seminario Dottorato ospita un seminario sui NUMERI PRIMI tenuto da Janos PINTZ, professore all'Alfred Renyi Institute della Hungarian Academy of Sciences.

Mercoledi 30 maggio 2007, aula 1BC/50, alle ore 15.00
Janos PINTZ (Hungarian Academy of Sciences)
"Landau's Problems on Primes"

-Abstract [vedi anche la Locandina PDF]:
At the 1912 Cambridge International Congress, Landau listed four basic problems about primes. These problems were characterised in his speech as unattackable at the present state of science''. The problems were the following.
(1) The Goldbach conjecture, that every even number exceeding 2 can be written as the sum of two primes.
(2) The Twin Prime Conjecture, the existence of infinitely many twin primes.
(3) Does there exist always at least one prime between neighbouring squares?
(4) Are there infinitely many primes p such that p-1 is a square?
All these problems are still open. In the lecture a survey will be given about partial results on problems (1)-(3), with special emphasis on the recent results of D. Goldston, C. Yildirim and the speaker on small gaps between primes.

Rif. int. C. Marastoni