Correlations of almost primes

Student thesis: Doctoral ThesisDoctor of Philosophy


We prove that analogues of the Hardy-Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula for the number of integers n = p1p2 X such that n + h is a product of exactly two primes which holds for almost all |h| ≤ H with (log X)19+εHX1−ε, under a restriction on the size of one of the prime factors of n and n + h. Additionally, we consider correlations n, n + h where n is a prime and n + h has exactly two prime factors, establishing an asymptotic formula which holds for almost all |h| ≤ H with X1/6+εHX1ε.
Date of Award1 Jan 2023
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorStephen Lester (Supervisor), Igor Wigman (Supervisor) & Abhishek Saha (Supervisor)

Cite this