On a problem of Hardy and Littlewood
On a question of P. Turán
On a ternary quadratic form over primes
On an almost pure sieve
On Bombieri's asymptotic sieve
On indefinite quadratic forms in four variables
On power-free numbers and polynomials. I.
On power.free numbers and polynomials. II.
On primitive divisors of Mersenne numbers
On Representing Integers as Products of the p + 1.
On Sieve method and Goldbach problem
On sums over primes
On the Brun-Titchmarsh theorem.
On the composition of the arithmetic functions σ and φ
On the constant β(k) in Rosser's sieve
On the coprimality of values of Euler's function at consecutive integers.
On the difference between consecutive prime numbers
On the Difference Between Consecutive Primes.
On the error term in the linear sieve
On the least almost-prime in arithmetic progression
Let denote an almost-prime with at most prime factors, counted according to multiplicity. Suppose that and are positive integers satisfying . Denote by the least almost-prime which satisfies . It is proved that for sufficiently large , there holds This result constitutes an improvement upon that of Iwaniec (1982), who obtained the same conclusion, but for the range in place of .