[Todos CMAT] Dos resultados de Teoría de Números
roma en fing.edu.uy
roma en fing.edu.uy
Dom Mayo 19 08:06:14 UYT 2013
Two Results in Number Theory
Two results announced this week relate to two long-unresolved problems:
the Twin Prime Conjecture and the Goldbach Conjecture.
- "Bounded gaps between primes," a paper by Yitang Zhang
(University of New Hampshire) shows that there are infinitely many
pairs of consecutive prime numbers that differ by a finite amount. In
the paper Zhang shows that there are an infinite number of consecutive
primes that differ by less than 70 million. It has been accepted by
the Annals of Mathematics . The proof represents progress on settling
the Twin Prime Conjecture, which states that there are infinitely many
prime numbers that differ by 2. In an article in emNew Scientist [
http://www.newscientist.com/article/dn23535-proof-that-an-infinite-number-of-primes-are-paired.html ] , Henry Iwaniec (Rutgers University) called Zhang's result
"beautiful."
- "Major arcs for Goldbach's theorem," a paper [
http://arxiv.org/abs/1305.2897 ] by Harald Helfgott (École Normale
Supérieure) is a proof of the Weak Goldbach Conjecture, which states
that every odd number greater than five can be written as the sum of
three primes. The Goldbach Conjecture states that every even number
greater than two can be written as the sum of two primes.
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