Twins almost prime under a Elliott-Halberstam's conjecture

We improve Bombieri’s asymptotic sieve to localise the variables. As a consequence, we prove, under a Elliott-Halberstam conjecture, that there exists an infinity of twins almost prime. Those are prime numbers $p$ such that for all $\epsilon >0$, $p-2$ is either a prime number or can be written as $p_1 p_2$where$p_1$and$p_2$areprimeand$p_1<X^{\varepsilon}$, and we give the explicit asymptotic.