## Dipartimento di Matematica## Università di Genova |

presso il Dipartimento di Matematica - aula 508

**Abstract**: 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 infinetely 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.

Per ulteriori informazioni rivolgersi a: Segreteria Scientifica DIMA, tel. 010-353 6965

e-mail: colloquium at dima.unige.it

Organizzato da: L.Robbiano, D.Arezzo, C. Bartocci, M.Cavaliere, A.Conca, L.Pusillo.

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