Almostprime ktuples
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 James Maynard (Oxford)
 Wednesday 21 November 2012, 16:0017:00
 MR11, CMS.
If you have a question about this talk, please contact Ben Green.
For $i=1,\dots,k$, let $L_i(n)=a_i n+b_i$ be linear functions
with integer coefficients, such that $\prod_{i=1}^{k L_i(n)$ has no fixed
prime divisor. It is conjectured that there are infinitely many integers
$n$ for which all of the $L_i(n)$ ($1\le i \le k$) are simultaneously
prime. Unfortunately we appear unable to prove this, but weighted sieves
all us to show that there are infinitely many integers $n$ for which
$\prod_[i=1}}k L_i(n)$ has at most $r_k$ prime factors, for some
explicit constant $r_k$ depending only on $k$. We describe new weighted
sieves which improve these bounds when $k\ge 3$, and discuss potential
applications to small prime gaps.
This talk is part of the Discrete Analysis Seminar series.
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