Almost-prime $k$-tuples

James Maynard

Let $k\ge 2$ and $\Pi (n)={\prod }_{i=1}^k(a_{i}n+b_i)$ for some integers $a_i,b_i$ ($1\le i\le k$). Suppose that $\Pi (n)$ has no fixed prime divisors. Weighted sieves have shown for infini…