Let $\Lambda$ be the von-Mangoldt function.
What is the estimate for the sum is
$$\sum_{\substack{1\leq x\leq n\\1\leq y\leq n}}\Lambda(x)\Lambda(y)=\psi(n)\psi(n)\sim n^2.$$
$\psi$ is the Chebyshev function.
But in twin prime conjecture for a fixed integer $a$,
$$\sum_{x\leq a} \Lambda(x)\Lamb...
Let $\Lambda$ be the von-Mangoldt function.
What is the estimate for the sum is
$$\sum_{\substack{1\leq x\leq n\\1\leq y\leq n}}\Lambda(x)\Lambda(y)=\psi(n)\psi(n)\sim n^2.$$
$\psi$ is the Chebyshev function.
But in twin prime conjecture for a fixed integer $a$,
$$\sum_{x\leq a} \Lambda(x)\Lamb...
