[Todos CMAT] Dos resultados de Teoría de Números

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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  

   - "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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