Explicit bounds for prime K-tuplets

Let $K\ge 2$ be a natural number and $a_i,b_i\in \mathbb{Z}$ for $i=1,\dots ,K-1$. We use the large sieve to derive explicit upper bounds for the number of prime $k$-tuplets, i.e., for the number of primes $p\le x$ for which all $a_{i}p+b_i$ are also prime.