I have seen this result in several places without an English reference:


There exist infinitely many primes $p$ such that $p-1=2q\_1q\_2$ where $q\_1$ and $q\_2$ are prime numbers with $q\_1,q\_2>p^{1/4}$.


There is a French reference (E. Bombieri. Le Grand Crible dans la Theorie Analytique des Nombres. Asterisque 18 Societe Mathematique de France 1974). However, I have not been able to find. I am wondering if someone knows an English reference for this claim or knows of similar results about small number of divisors of $p-1$. 


**Update:** the french reference produced in the answer does not include this statement. I expected the result to appear there as stated by Murty in [this article](https://web.math.ucsb.edu/~agboola/teaching/2005/winter/old-115A/murty.pdf) on page 14 he mentions this statement (with $1/4$ replaced by $\theta>1/4$) and asks the reader to consult the mentioned reference for 'technical details'. 



Reference Request for a result on divisors of $p-1$
If you allow $(p-1)/2$ to be prime, not just a product of two primes exceeding $p^{1/4+\epsilon}$, then the result is contained in somewhat stronger form in Heath-Brown: Artin's conjecture for primitive roots (Quart. J. Math. Oxford 37 (1986), 27-38). See Lemma 1 in that paper, and apply it with $k=1$, $u=3$, $v=16$. The result is based on the deep work of Bombieri-Friedlander-Iwaniec (1984). I believe this is the state-of-the-art. Heath-Brown also mentions that Gupta-Murty arrived at a similar conclusion but with at most three prime factors exceeding $p^{1/10+\epsilon}$.


