Resumen de Small gaps between primes
We introduce a refinement of the GPY sieve method for studying prime k -tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows us to show that for each k , the prime k -tuples conjecture holds for a positive proportion of admissible k -tuples. In particular, lim inf n (p n+m -p n )<8 for every integer m . We also show that lim inf(p n+1 -p n )=600 and, if we assume the Elliott-Halberstam conjecture, that lim inf n (p n+1 -p n )=12 and lim inf n (p n+2 -p n )=600 .
